Multifractal analysis of non-uniformly hyperbolic systems

被引:0
作者
Anders Johansson
Thomas M. Jordan
Anders Öberg
Mark Pollicott
机构
[1] University of Gävle,Divsion of Mathematics and Statistics
[2] University of Bristol,Department of Mathematics
[3] Uppsala University,Department of Mathematics
[4] University of Warwick,Mathematics Institute
来源
Israel Journal of Mathematics | 2010年 / 177卷
关键词
Lyapunov Exponent; Invariant Measure; Ergodic Theorem; Topological Entropy; Iterate Function System;
D O I
暂无
中图分类号
学科分类号
摘要
We prove a multifractal formalismfor Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.
引用
收藏
页码:125 / 144
页数:19
相关论文
共 17 条
[1]  
Barreira L.(2001)Variational principles and mixed multifractal spectra Transactions of the American Mathematical Society 353 3919-3944
[2]  
Saussol B.(2009)The Lyapunov spectrum of some parabolic systems Ergodic Theory and Dynamical Systems 29 919-940
[3]  
Gelfert K.(2002)Thermodynamic formalism and multifractal analysis of conformal infinite iterated function systems Acta Mathematica Hungarica 96 27-98
[4]  
Rams M.(1992)The Hausdorff dimension of an ergodic invariant measure for a piecewise monotonic map of the interval Canadadian Mathematical Bulletin 35 84-98
[5]  
Hanus P.(1980)Lyapunov exponents, entropy and periodic orbits for diffeomorphisms Publications Mathématiques. Institut de Hautes Études Scientifiques 51 137-173
[6]  
Mauldin D.(2004)A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups Ergodic Theory and Dynamical Systems 24 141-170
[7]  
Urbanski M.(2000)Multifractal formalism for some parabolic maps Ergodic theory and dynamical systems 20 843-857
[8]  
Hofbauer F.(2003)Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages Journal de Mathématiques Pures et Appliquées 82 1591-1649
[9]  
Raith P.(2003)On the variational principle for the topological entropy of certain non-compact sets Ergodic Theory and Dynamical Systems 23 317-348
[10]  
Katok A.(1996)Parabolic Cantor sets Fundamenta Mathematicae 151 241-277