Treffer: Statistical properties of nonuniformly expanding ID maps with logarithmic singularities

Title:
Statistical properties of nonuniformly expanding ID maps with logarithmic singularities
Authors:
TAKAHASI, Hiroki
Source:
Nonlinearity (Bristol. Print). 25(2):551-567
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 26 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, Equations différentielles, Ordinary differential equations, Equations aux dérivées partielles, Partial differential equations, 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, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse corrélation, Correlation analysis, Análisis correlación, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Cercle, Circle, Circulo, Corrélation, Correlation, Correlación, Décroissance exponentielle, Exponential decay, Decrecimiento exponencial, Dérivée, Derivative, Derivada, Etude statistique, Statistical study, Estudio estadístico, Inverse, Inverso, Mesure invariante, Invariant measure, Medida invariante, Mesure probabilité, Probability measure, Medida probabilidad, Non linéarité, Nonlinearity, No linealidad, Observable, Physique mathématique, Mathematical physics, Física matemática, Point critique, Critical point, Punto crítico, Point singulier, Singular point, Punto singular, Théorème central limite, Central limit theorem, Teorema central límite, Variance, Variancia, 28C10, 34C05, 35B38, 60B05, 60F05, 62H20, 62J10, Décomposition exponentielle, Ensemble positif, Mesure positive, Singularité logarithmique
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
ISSN:
0951-7715
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=25499531
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.25499531
Database:
PASCAL Archive

Weitere Informationen

We study the statistical properties of piecewise smooth maps on a circle, with a finite number of critical and singular points with an unbounded derivative, such that the derivative goes like the inverse of the distance to the singular points. We write down a simple set of conditions, and show that when these conditions are met, there exist an absolutely continuous invariant probability measure with exponential decay of correlations. We also rule out the existence of nontrivial coboundary, and obtain a positive variance in the central limit theorem for any nonconstant Holder continuous observable. Our results apply to a positive measure set of nonuniformly expanding maps on the circle considered by Takahasi and Wang (2012 Nonlinearity 25 533).