Dynamics of Foliations, Groups and Pseudogroups: 64 - Brossura

Walczak, Pawel

Brossura

ISBN 10: 3034896115 ISBN 13: 9783034896115

Casa editrice: Birkhäuser, 2012

Riassunto

This book deals with the dynamics of general systems such as foliations, groups and pseudogroups, systems which are closely related via the notion of holonomy. 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. Throughout the book, the reader will find a good number of inspirating problems related to the topics covered.

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Recensione

"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

 

Contenuti

1 Dynamical systems.- 1.1 Pseudogroups.- 1.2 First examples.- 1.3 Foliations, laminations and holonomy.- 1.4 Markov pseudogroups.- 1.5 Hyperbolic spaces and groups.- 2 Growth.- 2.1 Growth types.- 2.2 Growth in groups.- 2.3 Orbit growth for pseudogroups.- 2.4 Expansion growth.- 3 Entropy.- 3.1 Entropy of classical systems.- 3.1.1 Topological entropy of a transformation.- 3.1.2 Invariant measures.- 3.1.3 Measure-theoretic entropy.- 3.1.4 Examples.- 3.1.5 Variational principle.- 3.2 Entropy of pseudogroups.- 3.3 Geometric entropy of foliations.- 3.4 Relating various entropies.- 3.5 Examples and constructions.- 3.5.1 Pullback.- 3.5.2 Gluing.- 3.5.3 Turbulizat ion.- 3.6 Entropy and resiliency.- 4 Invariant measures.- 4.1 Basic definitions and facts.- 4.2 Transverse invariant measures and homology.- 4.3 Measures and orbit growth.- 4.4 Transverse invariant measures in codimension 1.- 4.5 Vanishing entropy and invariant measures.- 4.6 Entropy, geodesic flow and invariant measures.- 4.7 Harmonic measures.- 4.8 Patterson—Sullivan measures.- 5 Hausdorff dimension.- 5.1 Definitions and basic facts.- 5.2 Julia sets.- 5.3 Dimension in foliated manifolds.- 5.4 Dimension of a hyperbolic boundary.- 5.5 Dimension of a limit set.- 6 Varia.- 6.1 Complexity growth.- 6.2 Expansive systems.- 6.3 Pseudo-orbits and pseudoleaves.- 6.4 Generic leaves.

Dettagli dell?edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3034896115
• ISBN 13: 9783034896115
• Rilegatura: Copertina flessibile
• Numero di pagine: 244
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile