國立虎尾科技大學 |

Dynamical Systems on 2- and 3-Manifolds

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Dynamical Systems on 2- and 3-Manifolds/ by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka.
Author:	Grines, Viacheslav Z.
other author:	Medvedev, Timur V.
Description:	XXVI, 295 p. 95 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Topology. -
Online resource:	https://doi.org/10.1007/978-3-319-44847-3
ISBN:	9783319448473

Dynamical Systems on 2- and 3-Manifolds
Grines, Viacheslav Z.

Dynamical Systems on 2- and 3-Manifolds[electronic resource] /by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka. - 1st ed. 2016. - XXVI, 295 p. 95 illus.online resource. - Developments in Mathematics,461389-2177 ;. - Developments in Mathematics,41.

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.

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.

ISBN: 9783319448473

Standard No.: 10.1007/978-3-319-44847-3doiSubjects--Topical Terms:

633483
Topology.

LC Class. No.: QA611-614.97

Dewey Class. No.: 514

Dynamical Systems on 2- and 3-Manifolds
LDR:03865nam a22004095i 4500 001 972735
003 DE-He213
005 20200704110857.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319448473 $9 978-3-319-44847-3
024 7 $a 10.1007/978-3-319-44847-3 $2 doi
035 $a 978-3-319-44847-3
050 4 $a QA611-614.97
072 7 $a PBP $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBP $2 thema
082 0 4 $a 514 $2 23
100 1 $a Grines, Viacheslav Z. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1115814
245 1 0 $a Dynamical Systems on 2- and 3-Manifolds $h [electronic resource] / $c by Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XXVI, 295 p. 95 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Developments in Mathematics, $x 1389-2177 ; $v 46
505 0 $a 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.
520 $a 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.
650 0 $a Topology. $3 633483
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Differential equations. $3 527664
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Ordinary Differential Equations. $3 670854
700 1 $a Medvedev, Timur V. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1115815
700 1 $a Pochinka, Olga V. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1115816
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319448466
776 0 8 $i Printed edition: $z 9783319448480
776 0 8 $i Printed edition: $z 9783319831497
830 0 $a Developments in Mathematics, $x 1389-2177 ; $v 41 $3 1256322
856 4 0 $u https://doi.org/10.1007/978-3-319-44847-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)