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.
Publisher: Springer International Publishing AG
Number of pages: 295
Weight: 6092 g
Dimensions: 235 x 155 x 19 mm
Edition: 1st ed. 2016
"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)