Hofer, Helmut 1956
Overview
Works:  33 works in 153 publications in 2 languages and 2,205 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Editor, htt, Collector, Other, Honoree, Contributor 
Classifications:  QA614.83, 514.74 
Publication Timeline
.
Most widely held works by
Helmut Hofer
Symplectic invariants and Hamiltonian dynamics by
Helmut Hofer(
)
35 editions published between 1994 and 2011 in English and German and held by 871 WorldCat member libraries worldwide
The discoveries of the past decade have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mapƯ pings is very different from that of volume preserving mappings which raised new questions, many of them still unanswered. On the other hand, due to the analysis of an old variational principle in classical mechanics, global periodic phenomena in Hamiltonian systems have been established. As it turns out, these seemingly differƯ ent phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book which grew out of lectures given by the authors at Rutgers University, the RUB Bochum and at the ETH Zurich (1991) and also at the Borel Seminar in Bern 1992. Since the lectures did not require any previous knowledge, only a few and rather elementary topics were selected and proved in detail. Moreover, our seƯ lection has been prompted by a single principle: the action principle of mechanics. The action functional for loops in the phase space, given by 1 Fh) = J pdq J H(t, 'Y(t)) dt, 'Y 0 differs from the old Hamiltonian principle in the configuration space defined by a Lagrangian. The critical points of F are those loops 'Y which solve the Hamiltonian equations associated with the Hamiltonian H and hence are the periodic orbits
35 editions published between 1994 and 2011 in English and German and held by 871 WorldCat member libraries worldwide
The discoveries of the past decade have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mapƯ pings is very different from that of volume preserving mappings which raised new questions, many of them still unanswered. On the other hand, due to the analysis of an old variational principle in classical mechanics, global periodic phenomena in Hamiltonian systems have been established. As it turns out, these seemingly differƯ ent phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book which grew out of lectures given by the authors at Rutgers University, the RUB Bochum and at the ETH Zurich (1991) and also at the Borel Seminar in Bern 1992. Since the lectures did not require any previous knowledge, only a few and rather elementary topics were selected and proved in detail. Moreover, our seƯ lection has been prompted by a single principle: the action principle of mechanics. The action functional for loops in the phase space, given by 1 Fh) = J pdq J H(t, 'Y(t)) dt, 'Y 0 differs from the old Hamiltonian principle in the configuration space defined by a Lagrangian. The critical points of F are those loops 'Y which solve the Hamiltonian equations associated with the Hamiltonian H and hence are the periodic orbits
The Floer memorial volume by
Helmut Hofer(
Book
)
18 editions published in 1995 in English and German and held by 384 WorldCat member libraries worldwide
Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and farreaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, YangMills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder
18 editions published in 1995 in English and German and held by 384 WorldCat member libraries worldwide
Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and farreaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, YangMills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder
Geometry, analysis and probability : in honor of JeanMichel Bismut by
JeanBenoît Bost(
)
14 editions published between 2017 and 2018 in English and held by 295 WorldCat member libraries worldwide
This volume presents original research articles and extended surveys related to the mathematical interest and work of JeanMichel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S.K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian KI. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields
14 editions published between 2017 and 2018 in English and held by 295 WorldCat member libraries worldwide
This volume presents original research articles and extended surveys related to the mathematical interest and work of JeanMichel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S.K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian KI. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields
Lectures on geometry by
E Witten(
)
8 editions published between 2016 and 2017 in English and held by 203 WorldCat member libraries worldwide
This book contains a series of chapters by leading mathematicians on active are as of current research in geometry. Although not explicitly linked, the topics have a common flavor and appeal to anyone interested in recent developments in geometry. Taking the form of five chapters derived from lectures given at Clay Mathematics Institute events by leaders in the field, this book is intended to be accessible to all who work in this general area, regardless of their own particular research interests. Book jacket
8 editions published between 2016 and 2017 in English and held by 203 WorldCat member libraries worldwide
This book contains a series of chapters by leading mathematicians on active are as of current research in geometry. Although not explicitly linked, the topics have a common flavor and appeal to anyone interested in recent developments in geometry. Taking the form of five chapters derived from lectures given at Clay Mathematics Institute events by leaders in the field, this book is intended to be accessible to all who work in this general area, regardless of their own particular research interests. Book jacket
Holomorphic curves and global questions in contact geometry by
Casim Abbas(
)
15 editions published in 2019 in English and held by 177 WorldCat member libraries worldwide
This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory. An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9). The material is selfcontained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors
15 editions published in 2019 in English and held by 177 WorldCat member libraries worldwide
This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory. An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9). The material is selfcontained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors
Applications of polyfold theory I : the polyfolds of GromovWitten theory by
Helmut Hofer(
Book
)
12 editions published in 2017 in English and held by 145 WorldCat member libraries worldwide
In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyf
12 editions published in 2017 in English and held by 145 WorldCat member libraries worldwide
In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyf
Symplectic Invariants and Hamiltonian Dynamics by
Helmut Hofer(
)
4 editions published in 2011 in English and held by 28 WorldCat member libraries worldwide
The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a biinvariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology. The exposition is selfcontained and addressed to researchers and students from the graduate level onwards.  All the chapters have a nice introduction with the historic development of the subject and with a perfect description of the state of the art. The main ideas are brightly exposed throughout the book. (  ) This book, written by two experienced researchers, will certainly fill in a gap in the theory of symplectic topology. The authors have taken part in the development of such a theory by themselves or by their collaboration with other outstanding people in the area. (Zentralblatt MATH) This book is a beautiful introduction to one outlook on the exciting new developments of the last ten to fifteen years in symplectic geometry, or symplectic topology, as certain aspects of the subject are lately called. (  ) The authors are obvious masters of the field, and their reflections here and there throughout the book on the ambient literature and open problems are perhaps the most interesting parts of the volume. (Matematica)
4 editions published in 2011 in English and held by 28 WorldCat member libraries worldwide
The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a biinvariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology. The exposition is selfcontained and addressed to researchers and students from the graduate level onwards.  All the chapters have a nice introduction with the historic development of the subject and with a perfect description of the state of the art. The main ideas are brightly exposed throughout the book. (  ) This book, written by two experienced researchers, will certainly fill in a gap in the theory of symplectic topology. The authors have taken part in the development of such a theory by themselves or by their collaboration with other outstanding people in the area. (Zentralblatt MATH) This book is a beautiful introduction to one outlook on the exciting new developments of the last ten to fifteen years in symplectic geometry, or symplectic topology, as certain aspects of the subject are lately called. (  ) The authors are obvious masters of the field, and their reflections here and there throughout the book on the ambient literature and open problems are perhaps the most interesting parts of the volume. (Matematica)
A variational approach to a class of resonance problems with application to a wave equation problem by
Helmut Hofer(
Book
)
5 editions published in 1981 in English and held by 23 WorldCat member libraries worldwide
5 editions published in 1981 in English and held by 23 WorldCat member libraries worldwide
Employment effects of early interventions on job search programs by Andrea Weber(
)
2 editions published in 2004 in German and English and held by 16 WorldCat member libraries worldwide
2 editions published in 2004 in German and English and held by 16 WorldCat member libraries worldwide
Price and quantity adjustments in the Austrian labour market by
Helmut Hofer(
Book
)
4 editions published in 1998 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 9 WorldCat member libraries worldwide
Country employment policy reviews : Austria by
Karl Pichelmann(
Book
)
3 editions published in 1999 in English and held by 9 WorldCat member libraries worldwide
3 editions published in 1999 in English and held by 9 WorldCat member libraries worldwide
Wage mobility in Austria, 19861996 by
Helmut Hofer(
Book
)
1 edition published in 2001 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 6 WorldCat member libraries worldwide
Employment and wage adjustment in Euroland's labour market : a bird's eye view by
Helmut Hofer(
Book
)
1 edition published in 1999 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 6 WorldCat member libraries worldwide
Austria : longterm success through social partnership by Karl Pichelman(
Book
)
2 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
Computer use and the wage structure in Austria by
Helmut Hofer(
Book
)
2 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
Wage mobility in Austria 19861996 by
Helmut Hofer(
Book
)
2 editions published in 2001 in German and English and held by 3 WorldCat member libraries worldwide
2 editions published in 2001 in German and English and held by 3 WorldCat member libraries worldwide
Applications of symplectic geometry to Hamiltonian mechanics by Samuel Thomas Lisi(
)
1 edition published in 2006 in English and held by 3 WorldCat member libraries worldwide
In this thesis, we consider three applications of pseudoholomorphic curves to problems in Hamiltonian dynamics. In a first part, we prove an existence result for homoclinic orbits on a contacttype, critical energy level of an autonomous Hamiltonian, provided that the level is Hamiltonian displaceable. To do this, we transform the problem into a problem of Lagrangian intersection Floer theory. This involves a construction due to Mohnke [34] and some ideas from Legendrian surgery. In particular, we prove a generalization of Sere's result [36] on the existence of homoclinic orbits for an autonomous Hamiltonian system
1 edition published in 2006 in English and held by 3 WorldCat member libraries worldwide
In this thesis, we consider three applications of pseudoholomorphic curves to problems in Hamiltonian dynamics. In a first part, we prove an existence result for homoclinic orbits on a contacttype, critical energy level of an autonomous Hamiltonian, provided that the level is Hamiltonian displaceable. To do this, we transform the problem into a problem of Lagrangian intersection Floer theory. This involves a construction due to Mohnke [34] and some ideas from Legendrian surgery. In particular, we prove a generalization of Sere's result [36] on the existence of homoclinic orbits for an autonomous Hamiltonian system
Saisonale Muster von Beschäftigung und Arbeitslosigkeit in Österreich by
Franz Brandel(
Book
)
3 editions published in 1994 in German and held by 3 WorldCat member libraries worldwide
3 editions published in 1994 in German and held by 3 WorldCat member libraries worldwide
Some aspects of the theory of dynamical systems : a tribute to JeanChristophe Yoccoz by
Sylvain Crovisier(
Book
)
1 edition published in 2020 in English and held by 2 WorldCat member libraries worldwide
This is the first of two volumes which celebrate the memory of JeanChristophe Yoccoz. These volumes present research articles on various aspects of the theory of dynamical systems and related topics that were dear to him. [Source : 4ème de couv.]
1 edition published in 2020 in English and held by 2 WorldCat member libraries worldwide
This is the first of two volumes which celebrate the memory of JeanChristophe Yoccoz. These volumes present research articles on various aspects of the theory of dynamical systems and related topics that were dear to him. [Source : 4ème de couv.]
The Weinstein conjecture in P x Cl̳ by
Andreas Floer(
Book
)
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Zehnder, Eduard 1940 Other Collector Editor
 Floer, Andreas 19561991 Honoree Author Editor
 Taubes, Clifford 1954 Other Collector Editor
 Weinstein, Alan 1943 Other Collector Editor
 Zhang, Weiping 1964 Editor
 Bost, JeanBenoît 1961 Author Editor
 Labourie, François Editor
 Ma, Xiaonan Editor
 Le Jan, Y. (Yves) 1952 Editor
 Bismut, JeanMichel Honoree
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Associated Subjects
Austria Cell aggregationMathematics Complex manifolds Control theory Critical point theory (Mathematical analysis) Differentiable dynamical systems Differential equations, Partial European Union countries Geometry Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Global differential geometry GromovWitten invariants Hamiltonian systems Holomorphic functions Labor market Labor supply Manifolds (Mathematics) Manpower policy Mathematical analysis Mathematics Nonlinear operators Number theory Physics Probabilities Seasonal labor Seasonal unemployment Seasonal variations (Economics) Symplectic geometry Symplectic manifolds Topology Wages Wave equation
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Alternative Names
Helmut Hofer deutscher Mathematiker
Helmut Hofer Duits wiskundige
Helmut Hofer German mathematician
Helmut Hofer matemàtic alemany
Helmut Hofer matemático alemán
Helmut Hofer matematico tedesco
Helmut Hofer matematikan gjerman
Helmut Hofer mathématicien allemand
Helmut Hofer professor académico alemão
Helmut Hofer tysk matematikar
Helmut Hofer tysk matematiker
Hofer, H.
Hofer, H. 1956
Hofer, H. (Helmut), 1956
Hofer, Helmut
Hofer, Helmut H. W. 1956
Hofer, Helmut Hermann Walter 1956
Χέλμουτ Χόφερ
Хельмут Хофер американсконемецкий математик
هيلموت هوفر رياضياتي ألماني
ヘルムート・ホーファー ドイツの数学者
赫尔穆特·霍弗
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