Koli︠a︡da, S. F.
Overview
Works:  27 works in 91 publications in 2 languages and 2,120 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Other 
Classifications:  QA241, 512.7 
Publication Timeline
.
Most widely held works by
S. F Koli︠a︡da
Topics in dynamics and ergodic theory by
Sergey Bezuglyi(
)
15 editions published between 2003 and 2004 in English and held by 1,364 WorldCat member libraries worldwide
This book contains a collection of survey papers by leading researchers in ergodic theory, lowdimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2dimensional theory called pruning; the dynamics of Markov odometers, BratteliVershik diagrams and orbit equivalence of nonsingular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups
15 editions published between 2003 and 2004 in English and held by 1,364 WorldCat member libraries worldwide
This book contains a collection of survey papers by leading researchers in ergodic theory, lowdimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2dimensional theory called pruning; the dynamics of Markov odometers, BratteliVershik diagrams and orbit equivalence of nonsingular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups
Algebraic and topological dynamics : Algebraic and topological dynamics, May 1July 31, 2004, MaxPlanckInstitut für Mathematik,
Bonn, Germany by Conference on Algebraic and Topological Dynamics(
Book
)
17 editions published between 2005 and 2012 in English and held by 255 WorldCat member libraries worldwide
"This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the MaxPlanck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects." "Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statistical properties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems."BOOK JACKET
17 editions published between 2005 and 2012 in English and held by 255 WorldCat member libraries worldwide
"This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the MaxPlanck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects." "Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statistical properties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems."BOOK JACKET
Dynamical numbers : interplay between dynamical systems and number theory : a special program, May 1July 31, 2009 ; international
conference, July 2024, 2009, Max Planck Institute for Mathematics, Bonn, Germany by
S. F Koli︠a︡da(
Book
)
13 editions published between 2010 and 2012 in English and held by 225 WorldCat member libraries worldwide
13 editions published between 2010 and 2012 in English and held by 225 WorldCat member libraries worldwide
Dynamics and numbers : a special program, June 1July 31, 2014 : international conference, July 2125, 2014, Max Planck Institute
for Mathematics, Bonn, Germany by
Dynamics and Numbers(
Book
)
9 editions published in 2016 in English and held by 132 WorldCat member libraries worldwide
9 editions published in 2016 in English and held by 132 WorldCat member libraries worldwide
Geometry and dynamics of groups and spaces : in memory of Alexander Reznikov by
M. M Kapranov(
)
10 editions published in 2008 in English and held by 70 WorldCat member libraries worldwide
This book presents 18 articles by prominent mathematicians, dedicated to the memory of Alexander Reznikov (19602003), a brilliant highly original mathematician with broad mathematical interests. In addition it contains an influential, so far unpublished manuscript of Reznikov of book length. The research articles broadly reflect the range of Reznikov's own interests in geometry, group and number theory, functional analysis, dynamical systems and topology. In addition, there are surveys "Geometrization of probability," "Kleinian groups in higher dimensions," "(C, F)co
10 editions published in 2008 in English and held by 70 WorldCat member libraries worldwide
This book presents 18 articles by prominent mathematicians, dedicated to the memory of Alexander Reznikov (19602003), a brilliant highly original mathematician with broad mathematical interests. In addition it contains an influential, so far unpublished manuscript of Reznikov of book length. The research articles broadly reflect the range of Reznikov's own interests in geometry, group and number theory, functional analysis, dynamical systems and topology. In addition, there are surveys "Geometrization of probability," "Kleinian groups in higher dimensions," "(C, F)co
Dynamics of onedimensional maps by
A. N Sharkovskiĭ(
)
4 editions published between 1997 and 2010 in English and held by 21 WorldCat member libraries worldwide
Maps whose topological entropy is equal to zero (i.e., maps that have only cyeles of pe 2 riods 1,2,2 , ... ) are studied in detail and elassified. Various topological aspects of the dynamics of unimodal maps are studied in Chap ter 5. We analyze the distinctive features of the limiting behavior of trajectories of smooth maps. In particular, for some elasses of smooth maps, we establish theorems on the number of sinks and study the problem of existence of wandering intervals. In Chapter 6, for a broad elass of maps, we prove that almost all points (with respect to the Lebesgue measure) are attracted by the same sink. Our attention is mainly focused on the problem of existence of an invariant measure absolutely continuous with respect to the Lebesgue measure. We also study the problem of Lyapunov stability of dynamical systems and determine the measures of repelling and attracting invariant sets. The problem of stability of separate trajectories under perturbations of maps and the problem of structural stability of dynamical systems as a whole are discussed in Chap ter 7. In Chapter 8, we study oneparameter families of maps. We analyze bifurcations of periodic trajectories and properties of the set of bifurcation values of the parameter, in eluding universal properties such as Feigenbaum universality
4 editions published between 1997 and 2010 in English and held by 21 WorldCat member libraries worldwide
Maps whose topological entropy is equal to zero (i.e., maps that have only cyeles of pe 2 riods 1,2,2 , ... ) are studied in detail and elassified. Various topological aspects of the dynamics of unimodal maps are studied in Chap ter 5. We analyze the distinctive features of the limiting behavior of trajectories of smooth maps. In particular, for some elasses of smooth maps, we establish theorems on the number of sinks and study the problem of existence of wandering intervals. In Chapter 6, for a broad elass of maps, we prove that almost all points (with respect to the Lebesgue measure) are attracted by the same sink. Our attention is mainly focused on the problem of existence of an invariant measure absolutely continuous with respect to the Lebesgue measure. We also study the problem of Lyapunov stability of dynamical systems and determine the measures of repelling and attracting invariant sets. The problem of stability of separate trajectories under perturbations of maps and the problem of structural stability of dynamical systems as a whole are discussed in Chap ter 7. In Chapter 8, we study oneparameter families of maps. We analyze bifurcations of periodic trajectories and properties of the set of bifurcation values of the parameter, in eluding universal properties such as Feigenbaum universality
Dynamics and Numbers by
S. F Koli︠a︡da(
)
1 edition published in 2016 in English and held by 14 WorldCat member libraries worldwide
This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the MaxPlanck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties
1 edition published in 2016 in English and held by 14 WorldCat member libraries worldwide
This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the MaxPlanck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties
Dinamicheskie sistemy i nelineĭnye i︠a︡vlenii︠a︡ : sbornik nauchnykh trudov(
Book
)
2 editions published in 1990 in Russian and held by 8 WorldCat member libraries worldwide
2 editions published in 1990 in Russian and held by 8 WorldCat member libraries worldwide
Topics in dynamical systems and ergodic theory(
Book
)
1 edition published in 2003 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 7 WorldCat member libraries worldwide
On [omega]limit sets of triangular maps by
S. F Koli︠a︡da(
Book
)
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
On spatiotemporal chaos by
S. F Koli︠a︡da(
Book
)
1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide
On topological entropy when positivity implies + infinity by
S. F Koli︠a︡da(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this paper we study the relations between the properties of the topological semigroup of all continuous selfmaps S(X) on a compact metric space X (the topological group H(X) of all homeomorphisms on X) and possible values of the topological entropy of its elements. In particular, we prove that topological entropy of a functional envelope on the space of all continuous selfmaps on Peano continua or on compact metric spaces with continuum many connected components has only two possible values 0 and +1
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this paper we study the relations between the properties of the topological semigroup of all continuous selfmaps S(X) on a compact metric space X (the topological group H(X) of all homeomorphisms on X) and possible values of the topological entropy of its elements. In particular, we prove that topological entropy of a functional envelope on the space of all continuous selfmaps on Peano continua or on compact metric spaces with continuum many connected components has only two possible values 0 and +1
A dichotomy for minimal sets of fibrepreserving maps in graph bundles by
S. F Koli︠a︡da(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Minimal sets are studied for a compact dynamical system given by a fibrepreserving continuous map F in a graph bundle E (i.e., F is a skew product map). Given a closed set M in E we den̄e the set of socalled starlike interior points of M.A point in M is called an endpoint of M if it is not starlike interior. It is assumed that the base system is minimal (this assumption does not restrict generality when we are interested in the topological structure of minimal sets). The main theorem says that if M is a minimal set of F then the following dichotomy holds: The set of endpoints of M is either dense in M (and then M is nowhere dense in E), or it is empty (and then M has nonempty interior in E). Further, it is proved that in the latter case FjM is monotone on some subarcs of the b̄res. Since minimal sets of b̄represerving maps in tree bundles necessarily have endpoints, this theorem implies that these sets are nowhere dense, which in particular solves a problem of J. Smœđtal on minimal sets of triangular maps in the square
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Minimal sets are studied for a compact dynamical system given by a fibrepreserving continuous map F in a graph bundle E (i.e., F is a skew product map). Given a closed set M in E we den̄e the set of socalled starlike interior points of M.A point in M is called an endpoint of M if it is not starlike interior. It is assumed that the base system is minimal (this assumption does not restrict generality when we are interested in the topological structure of minimal sets). The main theorem says that if M is a minimal set of F then the following dichotomy holds: The set of endpoints of M is either dense in M (and then M is nowhere dense in E), or it is empty (and then M has nonempty interior in E). Further, it is proved that in the latter case FjM is monotone on some subarcs of the b̄res. Since minimal sets of b̄represerving maps in tree bundles necessarily have endpoints, this theorem implies that these sets are nowhere dense, which in particular solves a problem of J. Smœđtal on minimal sets of triangular maps in the square
Functional envelope of a dynamical system by Joseph Auslander(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
On dynamics of triangular maps of the square by
S. F Koli︠a︡da(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Analogues of AuslanderYorke theorems for multisensitivity(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract : We study multisensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. Our main result states that a minimal system is either multisensitive or an almost onetoone extension of its maximal equicontinuous factor. This is an analog of the AuslanderYorke dichotomy theorem: a minimal system is either sensitive or equicontinuous. Furthermore, we introduce the concept of a syndetically equicontinuous point, and we prove that a transitive system is either thickly sensitive or contains syndetically equicontinuous points, which is a refinement of another wellknown result of Akin, Auslander and Berg
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract : We study multisensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. Our main result states that a minimal system is either multisensitive or an almost onetoone extension of its maximal equicontinuous factor. This is an analog of the AuslanderYorke dichotomy theorem: a minimal system is either sensitive or equicontinuous. Furthermore, we introduce the concept of a syndetically equicontinuous point, and we prove that a transitive system is either thickly sensitive or contains syndetically equicontinuous points, which is a refinement of another wellknown result of Akin, Auslander and Berg
Shpargalka dli︠a︡ roditeleĭ by
S. F Koli︠a︡da(
Book
)
1 edition published in 1998 in Russian and held by 1 WorldCat member library worldwide
1 edition published in 1998 in Russian and held by 1 WorldCat member library worldwide
Algebraic and Topological Dynamics by
S. F Koli︠a︡da(
)
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
On the Lyapunov numbers by
S. F Koli︠a︡da(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval by
S. F Koli︠a︡da(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
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Audience Level
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Related Identities
 Bezuglyi, Sergey 1954 Author Editor
 MaxPlanckInstitut für Mathematik Other Organizer of meeting
 Manin, I︠U︡. I. Other Editor
 Ward, Thomas 1963 Other Editor
 Moree, Pieter Editor
 Kapranov, Mikhail Author
 Potyagailo, Leonid
 Möller, Martin Editor
 Sharkovskiĭ, A. N. (Aleksandr Nikolaevich) Author
 Fedorenko, V. V.
Associated Subjects
Aggressiveness in children Algebraic topology Autism in children Child psychotherapy Differentiable dynamical systems Differential equations Dynamics Ergodic theory Functional analysis Geometry Geometry, Differential Global analysis (Mathematics) Global differential geometry Group theory Hyperactive children Instytut matematyky (Akademii︠a︡ nauk Ukraïnsʹkoï RSR) Lowdimensional topology Manifolds (Mathematics) Mappings (Mathematics) Mathematics Measure theory Nonlinear systems Number theory Point mappings (Mathematics) Reznikov, Alexander, Topological algebras Topological dynamics Topological groups Topology Ukraine