Description
Springer Dynamics in One Dimension by Louis S. Block, William A. Coppel
The behaviour under iteration of unimodal maps of an_x000D_interval, such as the logistic map, has recently attracted_x000D_considerable attention. It is not so widely known that a_x000D_substantial theory has by now been built up for arbitrary_x000D_continuous maps of an interval. The purpose of the book is_x000D_to give a clear account of this subject, with complete_x000D_proofs of many strong, general properties. In a number of_x000D_cases these have previously been difficult of access. The_x000D_analogous theory for maps of a circle is also surveyed._x000D_Although most of the results were unknown thirty years ago,_x000D_the book will be intelligible to anyone who has mastered a_x000D_first course in real analysis. Thus the book will be of use_x000D_not only to students and researchers, but will also provide_x000D_mathematicians generally with an understanding of how simple_x000D_systems can exhibit chaotic behaviour._x000D_ Table of contents :- _x000D_
Periodic orbits.- Turbulence.- Unstable manifolds and homoclinic points.- Topological dynamics.- Topological dynamics (continued).- Chaotic and non-chaotic maps.- Types of periodic orbits.- Topological Entropy.- Maps of the circle._x000D_