Introduction to hyperbolic dynamics and ergodic theory
This is an introduction to hyperbolic dynamics and ergodic theory based on courses given by the author. It contains seven sections. Sections 1.1 and 1.2 include the most relevant examples and a historical sketch. Section 1.3 consists of an exposition of the topological dynamics of uniformly hyperbolic dynamical systems from the shadowing lemma to expansivity. The shadowing lemma is obtained as a consequence of a more general shadowing theorem whose proof is wisely deferred to the next section after much of the hyperbolic dynamics is obtained. Section 1.4 contains, besides the shadowing theorem, classical stability theorems. Section 1.5 is an exposition of the ergodic theory of hyperbolic sets including the Hopf argument. Section 1.6 provides the contraction-mapping principle and the stable manifold theorem and finally, Section 1.7 is a self-contained introduction to ergodic theory. The work contains also a very complete list of references. The clever structure of the text allows a clear and elegant presentation which makes this introduction a very valuable guide for those readers who approach the subject. For the entire collection see [Zbl 1395.37001].
scientific article; zbMATH DE number 6891919