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The Resource Dynamical Systems on 2- and 3-Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)

Dynamical Systems on 2- and 3-Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)

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Author
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Summary
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available
Language
eng
Work
Publication
Extent
XXVI, 295 p. 95 illus.
Contents
  • List of Symbols
  • Introduction
  • Further reading
  • 1. Introduction to dynamical systems
  • 2. General properties of the Morse-Smale diffeomorphisms
  • 3. The topological classification of the gradient-like diffeomorphism on surfaces
  • 4. Wild embedding on the separatrices into 3-manifolds and Pixton diffeomorphism
  • 5. The classification of the gradient-like diffeomorphisms on 3-manifolds
  • 6. Interrelation between the dynamics of Morse-Smale diffeormorphisms and the topology of the ambient 3-manifold
  • 7. An energy function for Morse-Smale diffeomorphisms on 3-manifolds
  • 8. The properties of nontrivial basic sets of A-diffeomorphisms related to type and dimension
  • 9. The classification of nontrivial basic sets of A-diffeomorphisms of surfaces
  • 10. Basic topological concepts of dynamical systems
  • Index
Isbn
9783319448473
Instance
Label
Dynamical Systems on 2- and 3-Manifolds
Title
Dynamical Systems on 2- and 3-Manifolds
Statement of responsibility
by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available
Member of
http://library.link/vocab/creatorName
Grines, Viacheslav Z
Image bit depth
0
LC call number
QA611-614.97
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Medvedev, Timur V.
  • Pochinka, Olga V.
  • SpringerLink
Series statement
Developments in Mathematics,
Series volume
46
http://library.link/vocab/subjectName
  • Mathematics
  • Dynamics
  • Ergodic theory
  • Differential equations
  • Topology
  • Mathematics
  • Topology
  • Dynamical Systems and Ergodic Theory
  • Ordinary Differential Equations
Label
Dynamical Systems on 2- and 3-Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
List of Symbols -- Introduction -- Further reading -- 1. Introduction to dynamical systems -- 2. General properties of the Morse-Smale diffeomorphisms -- 3. The topological classification of the gradient-like diffeomorphism on surfaces -- 4. Wild embedding on the separatrices into 3-manifolds and Pixton diffeomorphism -- 5. The classification of the gradient-like diffeomorphisms on 3-manifolds -- 6. Interrelation between the dynamics of Morse-Smale diffeormorphisms and the topology of the ambient 3-manifold -- 7. An energy function for Morse-Smale diffeomorphisms on 3-manifolds -- 8. The properties of nontrivial basic sets of A-diffeomorphisms related to type and dimension -- 9. The classification of nontrivial basic sets of A-diffeomorphisms of surfaces -- 10. Basic topological concepts of dynamical systems -- Index
Dimensions
unknown
Extent
XXVI, 295 p. 95 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319448473
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-44847-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-44847-3
Label
Dynamical Systems on 2- and 3-Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
List of Symbols -- Introduction -- Further reading -- 1. Introduction to dynamical systems -- 2. General properties of the Morse-Smale diffeomorphisms -- 3. The topological classification of the gradient-like diffeomorphism on surfaces -- 4. Wild embedding on the separatrices into 3-manifolds and Pixton diffeomorphism -- 5. The classification of the gradient-like diffeomorphisms on 3-manifolds -- 6. Interrelation between the dynamics of Morse-Smale diffeormorphisms and the topology of the ambient 3-manifold -- 7. An energy function for Morse-Smale diffeomorphisms on 3-manifolds -- 8. The properties of nontrivial basic sets of A-diffeomorphisms related to type and dimension -- 9. The classification of nontrivial basic sets of A-diffeomorphisms of surfaces -- 10. Basic topological concepts of dynamical systems -- Index
Dimensions
unknown
Extent
XXVI, 295 p. 95 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319448473
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-44847-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-44847-3

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