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The Resource Dynamical Systems on 2 and 3Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)
Dynamical Systems on 2 and 3Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)
Resource Information
The item Dynamical Systems on 2 and 3Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Dynamical Systems on 2 and 3Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2 and 3manifolds.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 3manifolds. 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
 Extent
 XXVI, 295 p. 95 illus.
 Contents

 List of Symbols
 Introduction
 Further reading
 1. Introduction to dynamical systems
 2. General properties of the MorseSmale diffeomorphisms
 3. The topological classification of the gradientlike diffeomorphism on surfaces
 4. Wild embedding on the separatrices into 3manifolds and Pixton diffeomorphism
 5. The classification of the gradientlike diffeomorphisms on 3manifolds
 6. Interrelation between the dynamics of MorseSmale diffeormorphisms and the topology of the ambient 3manifold
 7. An energy function for MorseSmale diffeomorphisms on 3manifolds
 8. The properties of nontrivial basic sets of Adiffeomorphisms related to type and dimension
 9. The classification of nontrivial basic sets of Adiffeomorphisms of surfaces
 10. Basic topological concepts of dynamical systems
 Index
 Isbn
 9783319448473
 Label
 Dynamical Systems on 2 and 3Manifolds
 Title
 Dynamical Systems on 2 and 3Manifolds
 Statement of responsibility
 by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka
 Language
 eng
 Summary
 This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2 and 3manifolds.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 3manifolds. 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
 http://library.link/vocab/creatorName
 Grines, Viacheslav Z
 Image bit depth
 0
 LC call number
 QA611614.97
 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 3Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)
 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 MorseSmale diffeomorphisms  3. The topological classification of the gradientlike diffeomorphism on surfaces  4. Wild embedding on the separatrices into 3manifolds and Pixton diffeomorphism  5. The classification of the gradientlike diffeomorphisms on 3manifolds  6. Interrelation between the dynamics of MorseSmale diffeormorphisms and the topology of the ambient 3manifold  7. An energy function for MorseSmale diffeomorphisms on 3manifolds  8. The properties of nontrivial basic sets of Adiffeomorphisms related to type and dimension  9. The classification of nontrivial basic sets of Adiffeomorphisms 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
 10.1007/9783319448473
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319448473
 Label
 Dynamical Systems on 2 and 3Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)
 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 MorseSmale diffeomorphisms  3. The topological classification of the gradientlike diffeomorphism on surfaces  4. Wild embedding on the separatrices into 3manifolds and Pixton diffeomorphism  5. The classification of the gradientlike diffeomorphisms on 3manifolds  6. Interrelation between the dynamics of MorseSmale diffeormorphisms and the topology of the ambient 3manifold  7. An energy function for MorseSmale diffeomorphisms on 3manifolds  8. The properties of nontrivial basic sets of Adiffeomorphisms related to type and dimension  9. The classification of nontrivial basic sets of Adiffeomorphisms 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
 10.1007/9783319448473
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319448473
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