منابع مشابه
Innnite Dimensional Srb Measures
We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an innnite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects the dynamical system of coupled maps on a d-dimensional lattice to an equilibrium statistical mechanical...
متن کاملErgodic theory of chaos and strange attractors
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the geometric theory of differentiable’dynamical systems, moderately excited chaotic systems require new tools, which are provided by the ergodic theory o f dynamical systems. This theory has reached a stage w...
متن کاملSRB-like Measures for C Dynamics
For any continuous map f : M → M on a compact manifold M , we define the SRB-like probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove that f has SRB-like measures, even if SRB measures do not exist. We prove that the definition of SRB-like measures is optimal, provided that the purpose of the researcher is to describe the asymptotic statistics for Lebesgue...
متن کاملSrb Measures for Certain Markov Processes
We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval with common fixed points at 0 and 1. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then theorems are given to analyze properties of the ergodic invariant measures δ0 and δ1. In particular, sufficien...
متن کاملSRB Measures for Infinite Dimensional Dynamical Systems
We study the existence of SRB measures and their properties for a class of infinite dimensional dynamical systems. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic, the system is topological mixing, and the splitting ...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2007
ISSN: 0387-3870
DOI: 10.3836/tjm/1184963660