LEADER 04764nam 22006255 450 001 9910150266203321 005 20220412233553.0 024 7 $a10.1007/978-3-319-44847-3 035 $a(CKB)3710000000938000 035 $a(DE-He213)978-3-319-44847-3 035 $a(MiAaPQ)EBC4741462 035 $a(PPN)197137504 035 $a(EXLCZ)993710000000938000 100 $a20161111d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDynamical systems on 2- and 3-manifolds /$fby Viacheslav Z. Grines, Timur V. Medvedev, Olga V. Pochinka 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XXVI, 295 p. 95 illus.) 225 1 $aDevelopments in Mathematics,$x1389-2177 ;$v46 311 $a3-319-44846-3 311 $a3-319-44847-1 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aList 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. 330 $aThis book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available. 410 0$aDevelopments in Mathematics,$x1389-2177 ;$v46 606 $aTopology 606 $aDynamics 606 $aErgodic theory 606 $aDifferential equations 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aTopology. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aDifferential equations. 615 14$aTopology. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aOrdinary Differential Equations. 676 $a515.352 700 $aGrines$b Viacheslav Z$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755888 702 $aMedvedev$b Timur V$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPochinka$b Olga V$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910150266203321 996 $aDynamical Systems on 2- and 3-Manifolds$92162743 997 $aUNINA