A Modern Introduction to Dynamical Systems

Richard Brown is a Teaching Professor and the Director of Undergraduate Studies in the Mathematics Department at Johns Hopkins University. His mathematical research involves using dynamical systems to study the topological and geometrical properties of surfaces. He is also active in studying and enhancing the effectiveness of undergraduate university education in mathematics and STEM and how students and educators navigate the difficult transition between secondary school mathematics and university mathematics.

• 1: What is a Dynamical System? 2: Simple Dynamics 3: The Objects of Dynamics 4: Flows and Maps of Euclidean Space 5: Recurrence 6: Phase Volume Preservation 7: Complicated Orbit Structure 8: Dynamical Invariants

This is a great introductory text for all students interested in the more mathematical aspects of nonlinear dynamics and chaos theory. I particularly recommend it to motivated students who consider specialising in dynamical systems theory. Whoever has mastered this book has an excellent overview of the modern understanding of the subject matter, has seen many interesting examples of various kinds of dynamical systems, and is well prepared to take up graduatelevel studies in this direction. Probably the author has written a new classic.