Ergodic Dynamics: From Basic Theory to Applications (Hardcover, 2021)

Preface.- The simplest examples.- Dynamical Properties of Measurable Transformations.- Attractors in Dynamical Systems.- Ergodic Theorems.- Mixing Properties of Dynamical Systems.- Shift Spaces.- Perron-Frobenius Theorem and Some Applications.- Invariant Measures.- No equivalent invariant measures: Type III maps.- Dynamics of Automorphisms of the Torus and Other Groups.- An Introduction to Entropy.- Complex Dynamics.- Maximal Entropy Measures on Julia Sets and a Computer Algorithm.- Cellular Automata.- Appendix A. Measures on Topological Spaces.- Appendix B. Integration and Hilbert Spaces.- Appendix C. Connections to Probability Theory.- Bibliography.- Index.