Dynamical Systems on 2- and 3-Manifolds
Authors: Grines, Viacheslav Z., Medvedev, Timur V., Pochinka, Olga V.
Free Preview- Discusses classical methods and approaches considered to be promising for the further research
- Presents main results on the topological classification of discrete dynamical systems
- Accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology
Buy this book
- About this book
-
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. - Reviews
-
“This book addresses the topological classification of smooth structurally stable discrete dynamical systems induced by a diffeomorphism on closed and orientable two- and three-dimensional manifolds. … The book is directed at experts, those trying to track down details of prior work, and others who wish to expand their expertise. The references are extensive. The authors have attempted to point the reader to more readily available sources when the original work is more difficult to find.” (William J. Satzer, MAA Reviews, maa.org, February, 2017)
- Table of contents (10 chapters)
-
-
Introduction to Dynamical Systems
Pages 1-26
-
General Properties of the Morse–Smale Diffeomorphisms
Pages 27-55
-
The Topological Classification of the Gradient-Like Diffeomorphism on Surfaces
Pages 57-75
-
Wild Embedding of the Separatrices into 3-Manifolds and Pixton Diffeomorphism
Pages 77-107
-
The Classification of the Gradient-Like Diffeomorphisms on 3-Manifolds
Pages 109-118
-
Table of contents (10 chapters)
- Download Sample pages 2 PDF (825.4 KB)
- Download Table of contents PDF (201.3 KB)
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- Dynamical Systems on 2- and 3-Manifolds
- Authors
-
- Viacheslav Z. Grines
- Timur V. Medvedev
- Olga V. Pochinka
- Series Title
- Developments in Mathematics
- Series Volume
- 46
- Copyright
- 2016
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-44847-3
- DOI
- 10.1007/978-3-319-44847-3
- Hardcover ISBN
- 978-3-319-44846-6
- Softcover ISBN
- 978-3-319-83149-7
- Series ISSN
- 1389-2177
- Edition Number
- 1
- Number of Pages
- XXVI, 295
- Number of Illustrations
- 95 b/w illustrations
- Topics
