Authors:
- Existing books on foliations deal mainly with either topology or Riemannian geometry of them; books on dynamics deal either with classical systems (single transformations or flows) or with groups.
- Here, dynamics of foliations (almost absent in the existing books) interplays with that of groups and pseudogroups
Part of the book series: Monografie Matematyczne (MONOGRAFIE, volume 64)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
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 inspirating problems related to the topics covered.
Reviews
"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
Authors and Affiliations
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Faculty of Mathematics, University of Łódź, Łódź, Poland
Paweł Walczak
Bibliographic Information
Book Title: Dynamics of Foliations, Groups and Pseudogroups
Authors: Paweł Walczak
Series Title: Monografie Matematyczne
DOI: https://doi.org/10.1007/978-3-0348-7887-6
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 2004
Hardcover ISBN: 978-3-7643-7091-6Published: 23 April 2004
Softcover ISBN: 978-3-0348-9611-5Published: 29 October 2012
eBook ISBN: 978-3-0348-7887-6Published: 06 December 2012
Series ISSN: 0077-0507
Series E-ISSN: 2297-0274
Edition Number: 1
Number of Pages: XI, 228
Topics: Group Theory and Generalizations, Topological Groups, Lie Groups, Dynamical Systems and Ergodic Theory, Differential Geometry