Treffer: Behaviour of the escape rate function in hyperbolic dynamical systems

Title:
Behaviour of the escape rate function in hyperbolic dynamical systems
Authors:
DEMERS, Mark F, WRIGHT, Paul
Source:
Nonlinearity (Bristol. Print). 25(7):2133-2150
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 3/4 p
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, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Variétés et complexes cellulaires, Manifolds and cell complexes, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Probabilités et statistiques, Probability and statistics, Statistiques, Statistics, Inférence à partir de processus stochastiques; analyse des séries temporelles, Inference from stochastic processes; time series analysis, 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, Borne supérieure, Upper bound, Cota superior, Difféomorphisme, Diffeomorphism, Difeomorfism, Fonction forme, Shape function, Función forma, Fonction taux, Rate function, Función tasa, Physique mathématique, Mathematical physics, Física matemática, Principe variationnel, Variational principle, Principio variacional, Système dynamique, Dynamical system, Sistema dinámico, Système hyperbolique, Hyperbolic system, Sistema hiperbólico, Trou, Hole, Hoyo, 37XX, 49S05, 57R50, 58D05, 58E30, 62M02, Continuité Hölder, Fonction hyperbolique, Mesure référence, Reference measure, Suite régulière
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics and Computer Science, Fairfield University, Fairfield, CT, United States
Department of Mathematics, University of Maryland, College Park, MD, United States
ISSN:
0951-7715
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26131768
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.26131768
Database:
PASCAL Archive

Weitere Informationen

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.