Treffer: Special ergodic theorems and dynamical large deviations

Title:
Special ergodic theorems and dynamical large deviations
Authors:
KLEPTSYN, Victor, RYZHOV, Dmitry, MINKOV, Stanislav
Source:
Nonlinearity (Bristol. Print). 25(11):3189-3196
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 17 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions réelles, Real functions, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Théorèmes limites, Limit theorems, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Difféomorphisme, Diffeomorphism, Difeomorfism, Dimension Hausdorff, Hausdorff dimension, Dimensión Hausdorff, Estimation moyenne, Mean estimation, Estimación promedio, Flot, Flow, Oleada, Fonction continue, Continuous function, Función continua, Grande déviation, Large deviation, Gran desviación, Mesure Lebesgue, Lebesgue measure, Medida Lebesque, Moyenne temporelle, Time average, Promedio temporal, Physique mathématique, Mathematical physics, Física matemática, Théorème ergodique, Ergodic theorem, Teorema ergódico, Zéro, Zero, Cero, 26A46, 37A30, 57R50, 58D05, 60F10, Application M, M map, Attracteur hyperbolique, Fonction test, Mesure SRB, SRB measure, Variété Riemann, Riemann manifold, Variété compacte, Compact manifold
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
CNRS, Institute of Mathematical Research of Rennes, IRMAR, UMR 6625 du CNRS, France
Chebyshev Laboratory, Department of Mathematics and Mechanics, St.-Petersburg State University, Russian Federation
Moscow State University, Faculty of Mechanics and Mathematics, GSP-1, Leninskie Gory, Moscow, 119991, Russian Federation
ISSN:
0951-7715
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26569534
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.26569534
Database:
PASCAL Archive

Weitere Informationen

Let f: M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function ϕ: M → ℝ and a constant α > 0, consider the set Kϕ,α of the initial points for which the Birkhoff time averages of the function ϕ differ from its μ―space average by at least α. As the measure μ is a global SRB one, the set Kϕ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.