“The authors make this monograph as accessible as possible. It is written to be usable as a text which is self-contained ... . This book caps decades of research on the subject and was written … that it might foster further investigation. ... The book pulls together a field which through war, cold war and happenstance had been disrupted and disconnected … . In doing so, this monograph coherently weaves together strands of a loose 90-year old tangle of ideas.” (Boris Hasselblatt, Mathematical Reviews, April, 2024)
This textbook offers a uniquely accessible introduction to flows on compact surfaces, filling a gap in the existing literature. The book can be used for a single semester course and/or for independent study. It demonstrates that covering spaces provide a suitable and modern setting for studying the structure of flows on compact surfaces. The thoughtful treatment of flows on surfaces uses topology (especially covering spaces), the classification of compact surfaces, and Euclidean and hyperbolic rigid motions to establish structural theorems that describe flows on surfaces generally. Several of the topics from dynamical systems that appear in this book (e. g., fixed points, invariant sets, orbits, almost periodic points) also appear in the many subareas of dynamical systems. The book successfully presents the reader with a self-contained introduction to dynamical systems or an expansion of one's existing knowledge of the field. Prerequisites include completion of a graduate-level topology course; a background in dynamical systems is not assumed.
