Shub, Michael 1943
Overview
Works:  78 works in 211 publications in 3 languages and 2,338 library holdings 

Genres:  Conference papers and proceedings Educational films Lectures Nonfiction films Speeches 
Roles:  Author, Editor, htt, Collector, Other, Contributor 
Classifications:  QA76, 511.3 
Publication Timeline
.
Most widely held works by
Michael Shub
Invariant manifolds by
Morris W Hirsch(
Book
)
21 editions published between 1977 and 2016 in 3 languages and held by 670 WorldCat member libraries worldwide
21 editions published between 1977 and 2016 in 3 languages and held by 670 WorldCat member libraries worldwide
Global stability of dynamical systems by
Michael Shub(
Book
)
43 editions published between 1978 and 1987 in 4 languages and held by 663 WorldCat member libraries worldwide
These notes are the result of a course in dynamical systems given at Orsay during the 197677 academic year. I had given a similar course at the Gradu ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's nStability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M
43 editions published between 1978 and 1987 in 4 languages and held by 663 WorldCat member libraries worldwide
These notes are the result of a course in dynamical systems given at Orsay during the 197677 academic year. I had given a similar course at the Gradu ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's nStability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M
From topology to computation : proceedings of the Smalefest by
Morris W Hirsch(
Book
)
19 editions published between 1990 and 2012 in English and held by 283 WorldCat member libraries worldwide
This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging over a wide variety of fields in pure and applied mathematics. In addition, Smale has provided an autobiographical essay, as well as a record of the lively panel discussions at the symposium. The research contributions include papers on differential topology, mathematical economics, dynamical systems, on the theory of computation, on nonlinear functional analysis, and on various applications in the physical and biological sciences. All are currently active areas of interdisciplinary research
19 editions published between 1990 and 2012 in English and held by 283 WorldCat member libraries worldwide
This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging over a wide variety of fields in pure and applied mathematics. In addition, Smale has provided an autobiographical essay, as well as a record of the lively panel discussions at the symposium. The research contributions include papers on differential topology, mathematical economics, dynamical systems, on the theory of computation, on nonlinear functional analysis, and on various applications in the physical and biological sciences. All are currently active areas of interdisciplinary research
Foundations of computational mathematics : selected papers of a conference held at Rio de Janeiro, January 1997 by
Felipe Cucker(
Book
)
13 editions published in 1997 in English and German and held by 239 WorldCat member libraries worldwide
This book contains articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics (FoCM) conference at IMPA in Rio de Janeiro in January 1997. FoCM brings together a novel constellation of subjects in which the computational process itself and the foundational mathematical underpinnings of algorithms are the objects of study. The conference was organized around nine workshops: systems of algebraic equations and computational algebraic geometry, homotopy methods and real machines, information based complexity, numerical linear algebra, approximation and PDE's, optimization, differential equations and dynamical systems, relations to computer science and vision and related computational tools. The book gives the reader an idea of the state of the art in this emerging discipline
13 editions published in 1997 in English and German and held by 239 WorldCat member libraries worldwide
This book contains articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics (FoCM) conference at IMPA in Rio de Janeiro in January 1997. FoCM brings together a novel constellation of subjects in which the computational process itself and the foundational mathematical underpinnings of algorithms are the objects of study. The conference was organized around nine workshops: systems of algebraic equations and computational algebraic geometry, homotopy methods and real machines, information based complexity, numerical linear algebra, approximation and PDE's, optimization, differential equations and dynamical systems, relations to computer science and vision and related computational tools. The book gives the reader an idea of the state of the art in this emerging discipline
The mathematics of numerical analysis : 1995 AMSSIAM Summer Seminar in Applied Mathematics, July 17August 11, 1995, Park
City, Utah by AMSSIAM Summer Seminar in Applied Mathematics(
Book
)
11 editions published between 1995 and 1996 in English and held by 226 WorldCat member libraries worldwide
11 editions published between 1995 and 1996 in English and held by 226 WorldCat member libraries worldwide
Complexity and real computation by
Lenore Blum(
)
5 editions published between 1984 and 1998 in English and held by 90 WorldCat member libraries worldwide
Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space. The objects of study are algorithms defined within a formal model of computation. Upper bounds on the computational complexity of a problem are usually derived by constructing and analyzing specific algorithms. Meaningful lower bounds on computational complexity are harder to come by, and are not available for most problems of interest. The dominant approach in complexity theory is to consider algorithms as oper ating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot rep resent real or complex numbers, unless the numbers are rounded to approximate values from a discrete set. A major concern of the theory is the number of com putation steps required to solve a problem, as a function of the length of the input string
5 editions published between 1984 and 1998 in English and held by 90 WorldCat member libraries worldwide
Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space. The objects of study are algorithms defined within a formal model of computation. Upper bounds on the computational complexity of a problem are usually derived by constructing and analyzing specific algorithms. Meaningful lower bounds on computational complexity are harder to come by, and are not available for most problems of interest. The dominant approach in complexity theory is to consider algorithms as oper ating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot rep resent real or complex numbers, unless the numbers are rounded to approximate values from a discrete set. A major concern of the theory is the number of com putation steps required to solve a problem, as a function of the length of the input string
Stable ergodicity and julienne quasiconformality by
Charles Pugh(
Book
)
3 editions published between 1997 and 2000 in English and held by 8 WorldCat member libraries worldwide
Abstract: "In this paper we eliminate some of the most nettlesome hypotheses of our previous article, 'Stably ergodic dynamical systems and partial hyperbolicity' [22], and expand the domain of stably ergodic, partially hyperbolic dynamical systems to include all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property. Our main tool is a new concept  julienne quasi conformality of the stable and unstable holonomy maps. An important feature of this is that the holonomy maps preserve all julienne density points."
3 editions published between 1997 and 2000 in English and held by 8 WorldCat member libraries worldwide
Abstract: "In this paper we eliminate some of the most nettlesome hypotheses of our previous article, 'Stably ergodic dynamical systems and partial hyperbolicity' [22], and expand the domain of stably ergodic, partially hyperbolic dynamical systems to include all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property. Our main tool is a new concept  julienne quasi conformality of the stable and unstable holonomy maps. An important feature of this is that the holonomy maps preserve all julienne density points."
Stably ergodic approximation : two examples by
Michael Shub(
Book
)
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volumepreserving, partiallyhyperbolic diffeomorphisms of a compact manifold. In this paper we deal with two recalcitrant examples; the standard map cross Anosov and the ergodic automorphisms of the four torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property."
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volumepreserving, partiallyhyperbolic diffeomorphisms of a compact manifold. In this paper we deal with two recalcitrant examples; the standard map cross Anosov and the ergodic automorphisms of the four torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property."
Foundations of Computational Mathematics : Selected Papers of a Conference Held at Rio de Janeiro, January 1997(
)
in English and held by 7 WorldCat member libraries worldwide
in English and held by 7 WorldCat member libraries worldwide
Global Stability of Dynamical Systems by
Michael Shub(
)
in English and held by 7 WorldCat member libraries worldwide
in English and held by 7 WorldCat member libraries worldwide
A stably Bernoullian diffeomorphism that is not Anosov by
Michael Shub(
Book
)
2 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
From Topology to Computation: Proceedings of the Smalefest(
)
in English and held by 7 WorldCat member libraries worldwide
in English and held by 7 WorldCat member libraries worldwide
Newton and predictorcorrector methods for overdetermined systems of equations by J. P Dedieu(
Book
)
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Complexity theoretic aspects of continuation methods for the solution of square or underdetermined systems of polynomial equations have been studied by various authors. In this paper we consider overdetermined systems where there are more equations than unknowns. We take two approaches to the problem. In the first we study Newton's method for an overdetermined system and then apply it to the elements of a path in the space of problems to produce a path of solutions. In the second we study the map from the variety of solutions to the variety of problems and use its structure to lift a path of problems to solutions. We call these second methods predictorcorrector methods."
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Complexity theoretic aspects of continuation methods for the solution of square or underdetermined systems of polynomial equations have been studied by various authors. In this paper we consider overdetermined systems where there are more equations than unknowns. We take two approaches to the problem. In the first we study Newton's method for an overdetermined system and then apply it to the elements of a path in the space of problems to produce a path of solutions. In the second we study the map from the variety of solutions to the variety of problems and use its structure to lift a path of problems to solutions. We call these second methods predictorcorrector methods."
On simple double zeros and badly conditioned zeros of analytic functions of n variables by
Thomas J. Watson IBM Research Center(
Book
)
4 editions published in 1999 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1999 in English and held by 6 WorldCat member libraries worldwide
Stable ergodicity and stable accessibility by
Charles Pugh(
Book
)
2 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we discuss how a little hyperbolicity goes a long way towards guaranteeing stable ergodicity. Examples to which our theory applies include translations on certain homogeneous spaces and the time one map of the geodesic flow for a manifold of constant negative curvature. We also discuss the role played by a concept from control theory, accessibility by paths tangent to a pair of subbundles of the tangent bundle."
2 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we discuss how a little hyperbolicity goes a long way towards guaranteeing stable ergodicity. Examples to which our theory applies include translations on certain homogeneous spaces and the time one map of the geodesic flow for a manifold of constant negative curvature. We also discuss the role played by a concept from control theory, accessibility by paths tangent to a pair of subbundles of the tangent bundle."
The identity is best for 2 x 2 real matrices by
Debra J Lewis(
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
Stable ergodicity in homogeneous spaces by
Jonathan Brezin(
Book
)
1 edition published in 1995 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 4 WorldCat member libraries worldwide
The story of the higher dimensional Poincaré conjecture : what actually happened on the beaches of Rio de Janeiro by
Stephen Smale(
Visual
)
1 edition published in 2009 in English and held by 4 WorldCat member libraries worldwide
Smale talks about Poincaré conjecture and the controversy about his proof. He provides personal experiences surrounding his work and its relationship to government policies
1 edition published in 2009 in English and held by 4 WorldCat member libraries worldwide
Smale talks about Poincaré conjecture and the controversy about his proof. He provides personal experiences surrounding his work and its relationship to government policies
On a theory of computation over the real numbers : NP completeness, recursive functions and universal machines by
Lenore Blum(
Book
)
3 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
On a theory of computation and complexity over the real numbers : NP completeness, recursive functions and universal machines by
Lenore Blum(
Book
)
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
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Related Identities
 Hirsch, Morris W. 1933 Author Editor Collector
 Pugh, C. C. (Charles Chapman) 1940
 Smale, Stephen 1930 Other Editor Honoree
 Fathi, Albert Other Editor Contributor
 Langevin, Remi Other Editor Contributor
 Cucker, Felipe 1958 Other Editor Author Contributor Collector
 Marsden, Jerrold E. Collector Editor
 Renegar, James 1955 Other Editor
 Blum, Lenore Author
 Christy, Joseph Translator
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Associated Subjects
Algebra Bernoulli shifts Cell aggregationMathematics Complex manifolds Computable functions Computational complexity Computer algorithms Computer science Computer software Continuation methods Determinants Differentiable dynamical systems Differential equations Differential topology Ergodic theory Exponential functions Foliations (Mathematics) Geometry Geometry, Differential Global analysis (Mathematics) Hermitian operators Homogeneous spaces Homology theory Information theory Invariant manifolds Invariants Logic, Symbolic and mathematical Manifolds (Mathematics) Mathematical analysis Mathematics MathematicsData processing Matrices Morphisms (Mathematics) NewtonRaphson method NPcomplete problems Number theory Numerical analysis Numerical calculations Poincaré, Henri, Poincaré conjecture Poincaré series Polynomials Realtime data processing Recursive functions Riemannian manifolds Singularities (Mathematics) Smale, Stephen, Stability Submanifolds Topological dynamics
Covers
Alternative Names
Michael Shub American mathematician
Michael Shub Amerikaans wiskundige
Michael Shub matamaiticeoir Meiriceánach
Michael Shub matemàtic estatunidenc
Michael Shub matemático estadounidense
Michael Shub matematico statunitense
Michael Shub matemáticu estauxunidense
Michael Shub matematikan amerikan
Michael Shub mathématicien américain
Michael Shub USamerikanischer Mathematiker
Shub, M.
Shub, M. 1943
Shub, M. (Michael)
Shub, M. (Michael), 1943
Shub, Michael 1942
Shub, Michael Ira
Shub, Michael Ira 1943
Shub, Mike
ميتشايل شوب
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