Dynamics Beyond Uniform Hyperbolicity

A Global Geometric and Probabilistic Perspective

Christian Bonatti, Lorenzo J. Diaz, Marcelo Viana - Collection Encyclopaedia of Mathematical Sciences

384 pages, parution le 14/10/2004

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Résumé

The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically. Another revolution has been taking place in the last couple of decades, as one tries to build a global theory for "most" dynamical systems, recovering as much as possible of the conclusions of the uniformly hyperbolic case, in great generality. This book aims to put such recent developments in a unified perspective, and to point out open problems and likely directions for further progress. It is aimed at researchers, both young and senior, willing to get a quick, yet broad, view of this part of dynamics. Main ideas, methods, and results are discussed, at variable degrees of depth, with references to the original works for details and complementary information.

Written for: For graduate students and researchers in mathematics and physics

Sommaire

Hyperbolicity and Beyond
One-Dimensional Dynamics
Homoclinic Tangencies:
Henon-like Dynamics
Non-Critical Dynamics and Hyperbolicity
Heterodimensional Cycles and Blenders
Robust Transitivity
Stable Ergodicity
Robust Singular Dynamics
Generic Diffeomorphisms
SRB Measures and Gibbs States
Lyapunov Exponents

A. Perturbation Lemmas
B. Normal Hyperbolicity and Foliations
C. Non-Uniformly Hyperbolic Theory
D. Random Perturbations
E. Decay of Correlations
Conclusion

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Christian Bonatti, Lorenzo J. Diaz, Marcelo Viana
Collection	Encyclopaedia of Mathematical Sciences
Parution	14/10/2004
Nb. de pages	384
Format	16 x 24
Couverture	Relié
Poids	715g
Intérieur	Noir et Blanc
EAN13	9783540220664