Ergodic Dynamics

Jane Hawkins is Professor Emerita at the University of North Carolina at Chapel Hill. She obtained her Ph.D. from the University of Warwick, where she studied as a Marshall Scholar. Her research interests are centered on dynamical systems and complex dynamics, including cellular automata and Julia sets. She has taught graduate courses related to the text at Stony Brook University, Cal Tech, Duke and UNC. In addition to supervising more than a dozen Ph.D. and master’s students, Hawkins was an inaugural Fellow of the American Mathematical Society where she has also been active in AMS governance.

• 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.

“This is a stylish and easy-to-read exposition of some major aspects of current ergodic theory. … I would strongly recommend this book for someone wishing to understand the themes of modern ergodic theory and dynamical systems, and certainly as a source for teaching advanced courses in these areas. It also makes interesting reading for current researchers.” (A. H. Dooley, SIAM Review, Vol. 64 (3), September, 2022)“A book like this one is a very useful tool to introduce this subject, in a didactic way, for students and young researchers … . The book is intended for an introductory course on the main ideas and examples in ergodic theory … using some classical and current applications. A solid grounding in measure theory, topology, and complex analysis will make the book readily accessible. There are exercises given at the end of every chapter, including the appendices.” (Elismar daRosa Oliveira, Mathematical Reviews, April, 2022)