Finite rank approximations of expanding maps with neutral singularities
نویسنده
چکیده
For a class of expanding maps with neutral singularities we prove the validity of a finite rank approximation scheme for the analysis of Sinai-Ruelle-Bowen measures. Earlier results of this sort were known only in the case of hyperbolic systems. AMS Subject Classification: Primary 37M25, 37A40; Secondary 37A30, 37A50, 37C30.
منابع مشابه
Perron—frobenius Spectrum for Random Maps and Its Approximation
To study the convergence to equilibrium in random maps, we develop the spectral theory of the corresponding transfer (Perron— Frobenius) operators acting in a certain Banach space of generalized functions (distributions). The random maps under study in a sense fill the gap between expanding and hyperbolic systems, since among their (deterministic) components there are both expanding and contrac...
متن کاملJa n 20 06 LARGE DEVIATIONS FOR NON - UNIFORMLY EXPANDING MAPS
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hy-perbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of...
متن کاملSolution of Harmonic Problems with Weak Singularities Using Equilibrated Basis Functions in Finite Element Method
In this paper, Equilibrated Singular Basis Functions (EqSBFs) are implemented in the framework of the Finite Element Method (FEM), which can approximately satisfy the harmonic PDE in homogeneous and heterogeneous media. EqSBFs are able to automatically reproduce the terms consistent with the singularity order in the vicinity of the singular point. The newly made bases are used as the compliment...
متن کاملStatistical Properties of Nonequilibrium Dynamical Systems
We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our work covers systems that admit a finite SRB measure and it also covers systems that admit an infinite SRB measure. In particular, we obtain a linear response formula for both finite and infinite SRB measures. We apply our results to interval maps with a neutral fixed p...
متن کامل2 00 6 Large Deviations for Non - Uniformly Expanding Maps
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hy-perbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of...
متن کامل