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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)
Resource Information
The item Dynamical Systems on 2- and 3-Manifolds, 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 3-Manifolds, 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 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
- 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
- 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
- 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
- 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)
- 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)
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.bu.edu/portal/Dynamical-Systems-on-2--and-3-Manifolds-by/Jw8rRDFhygM/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/Dynamical-Systems-on-2--and-3-Manifolds-by/Jw8rRDFhygM/">Dynamical Systems on 2- and 3-Manifolds, by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka, (electronic resource)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>