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Field name	Details
Dewey Class	514
Title	Dynamical Systems on 2- and 3-Manifolds ([EBook]) / by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka.
Author	Grines, Viacheslav Z.
Added Personal Name	Medvedev, Timur V. author.
Added Personal Name	Pochinka, Olga V. author.
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	XXVI, 295 p. 95 illus. : online resource.
Series	Developments in mathematics 1389-2177 ; ; 46
ISBN	9783319448473
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-44847-3
Links to Related Works	Subject References: Differential Equations . Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Mathematics . Ordinary differential equations . Topology . Authors: Grines, Viacheslav Z. . Medvedev, Timur V. . Pochinka, Olga V. . Corporate Authors: SpringerLink (Online service) . Series: Developments in mathematics . Classification: 514 .

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Dynamical Systems on 2- and 3-Manifolds

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