Related papers: Quenched Mixing Rates for Doubly Intermittent Maps
We study rates of mixing for small random perturbations of one dimensional Lorenz maps. Using a random tower construction, we prove that, for Holder observables, the random system admits exponential rates of quenched correlation decay.
We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…
We consider a family $\mathcal F$ of maps with two branches and a common neutral fixed point $0$ such that the order of tangency at $0$ belongs to some interval $[\alpha_0, \alpha_1]\subset (0, 1)$. Maps in $\mathcal F$ do not necessarily…
We obtain quenched almost sure invariance principle (with convergence rate) for Random Young Tower. We apply our result to i.i.d perturbations of non-uniformly expanding maps. In particular, we answer one open question in \cite{BBM}.
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps $T_\alpha$ using the full parameter range $0<…
We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding…
We consider a class of doubly intermittent maps with critical points, unbounded derivative and regularly varying tails. Under some mild assumptions we prove the existence of a unique mixing absolutely continuous invariant measure and give…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
We prove a quenched almost sure invariance principle for certain classes of random distance expanding dynamical systems which do not necessarily exhibit uniform decay of correlations.
In this paper, we consider the quenched invariance principle for random Young towers driven by an ergodic system. In particular, we obtain the Wassertein convergence rate in the quenched invariance principle. As a key ingredient, we derive…
We develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows. Previously, such results were restricted to the situation where there is a first return Poincar\'e map that…
We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two…
This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the…
In this paper, we prove several theorems relating annealed exponential mixing of the two-point motion with quenched properties of the one-point motion for conservative IID random dynamical systems. In particular, we show that annealed…
We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of…
We study the phenomenon of intermittency in inhomogeneous lattices of coupled map where inhomogeneity appears in the form of different values of map parameters at adjacent sites.The system exhibits spatiotemporal intermittency in various…
In this article we study random tower maps driven by an ergodic automorphism. We prove quenched exponential correlations decay for tower maps admitting exponential tails. Our technique is based on constructing suitable cones of functions,…
We study random dynamical systems composed of LSV maps with varying parameters, without any mixing assumptions on the base space of random dynamics. We establish a quenched central limit theorem and identify conditions under which the…