Multifractal analysis of non-uniformly hyperbolic systems
نویسندگان
چکیده
We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville–Pomeau map.
منابع مشابه
J an 2 00 8 MULTIFRACTAL ANALYSIS OF NON - UNIFORMLY HYPERBOLIC SYSTEMS
We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville–Pomeau map.
متن کاملSe p 20 08 MULTIFRACTAL ANALYSIS OF NON - UNIFORMLY HYPERBOLIC SYSTEMS
We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville–Pomeau map.
متن کاملThe Thermodynamic Approach to Multifractal Analysis
Most results in multifractal analysis are obtained using either a thermodynamic approach based on existence and uniqueness of equilibrium states or a saturation approach based on some version of the specification property. A general framework incorporating the most important multifractal spectra was introduced by Barreira and Saussol, who used the thermodynamic approach to establish the multifr...
متن کاملMultifractal Analysis of Lyapunov Exponent for Continued Fraction and Manneville–Pomeau Transformations and Applications to Diophantine Approximation
We extend some of the theory of multifractal analysis for conformal expanding systems to two new cases: The non-uniformly hyperbolic example of the Manneville– Pomeau equation and the continued fraction transformation. A common point in the analysis is the use of thermodynamic formalism for transformations with infinitely many branches. We effect a complete multifractal analysis of the Lyapunov...
متن کاملHistoric set carries full hausdorff dimension
We prove that the historic set for ratio of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional non-uniformly hyperbolic dynamical systems.
متن کامل