# Groups of Circle Diffeomorphisms

In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. *Groups of Circle Diffeomorphisms* systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.

**Rostislav Grigorchuk, Texas A&M University, and Etienne Ghys, École Normale Supérieure de Lyon**

“This is a wonderful book about ‘mildly’ smooth actions of groups on the most important manifolds in mathematics: the circle and the line. Andrés Navas draws upon the classical contributions of Poincaré, Denjoy, Hölder, Plante, Thompson, Sacksteder, and Duminy, as well as the relatively recent achievements of Margulis and Witte Morris, to offer the first book-length exploration of this topic. The analytic techniques, the dynamical point of view, and the algebraic nature of objects considered here produce a blend of beautiful mathematics that will be used by researchers in several areas of science.”

**Takashi Tsuboi, University of Tokyo**

“*Groups of Circle Diffeomorphisms* provides a great overview of the research on differentiable group actions on the circle. Navas’s book will appeal to those doing research on differential topology, transformation groups, dynamical systems, foliation theory, and representation theory, and will be a solid base for those who want to further attack problems of group actions on higher dimensional manifolds or of geometric group theory.”

**Physical Sciences: **
Theoretical Physics

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