Foliations, groups and pseudogroups are objects which are closely related via the notion of holonomy. In the 1980s they became considered as general dynamical systems. This book deals with their dynamics. Since "dynamics" is a very extensive term, we focus on some of its aspects only. Roughly speaking, we concentrate on notions and results related to different ways of measuring complexity of the systems under consideration. More precisely, we deal with different types of growth, entropies and dimensions of limiting objects. Invented in the 1980s (by E. Ghys, R. Langevin and the author) geometric entropy of a foliation is the principal object of interest among all of them.
Throughout the book, the reader will find a good number of insipiring problems related to the topics covered.
"The classical theory of dynamical systems has been greatly generalized to the rich context of foliations and actions of groups and pseudogroups on spaces. The book under review expounds on this theory in considerable detail... Much of the material in this book is pertinent to applied mathematics... Experts in control systems also recognize foliation theory as a cognate subject of some interest... With the phenomenal interaction between pure and applied mathematics over recent decades, this book should be of considerable interest to many application-oriented mathematicians." --SIAM Book Reviews