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We introduce random towers to study almost sure rates of correlation decay for random partially hyperbolic attractors. Using this framework, we obtain abstract results on almost sure exponential, stretched exponential and polynomial correlation decay rates. We then apply our results to small random perturbations of Axiom A attractors, small perturbations of derived from Anosov partially hyperbolic systems and to solenoidal attractors with random intermittency.
The family of pairwise independently determined (PID) systems, i.e. those for which the independent joining is the only self joining with independent 2-marginals, is a class of systems for which the long standing open question by Rokhlin, of whether
In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.
Suppose $(f,mathcal{X},mu)$ is a measure preserving dynamical system and $phi colon mathcal{X} to mathbb{R}$ a measurable function. Consider the maximum process $M_n:=max{X_1 ldots,X_n}$, where $X_i=phicirc f^{i-1}$ is a time series of observations o
We prove that any strongly mixing action of a countable abelian group on a probability space has higher order mixing properties. This is achieved via introducing and utilizing $mathcal R$-limits, a notion of convergence which is based on the classica
In this paper, unstable metric entropy, unstable topological entropy and unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. A version of Shannon-McMillan-Breiman Theorem is established, and a variational princip