Related papers: Global-local mixing for infinite measure dynamical…

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…

In the context of 'infinite-volume mixing' we prove global-local mixing for the Boole map, a.k.a. Boole transformation, which is the prototype of a non-uniformly expanding map with two neutral fixed points. Global-local mixing amounts to…

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 study the property of global-local mixing for full-branched expanding maps of either the half-line or the interval, with one indifferent fixed point. Global-local mixing expresses the decorrelation of global vs local observables w.r.t.…

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…

In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…

In this article we show that a large class of infinite measure preserving dynamical systems that do not admit physical measures nevertheless exhibit strong statistical properties. In particular, we give sufficient conditions for existence…

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…

We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a…

In the scope of the statistical description of dynamical systems, one of the defining features of chaos is the tendency of a system to lose memory of its initial conditions (more precisely, of the distribution of its initial conditions).…

We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on…

In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…

We analyze the connections between the non-Markovianity degree of the most general phase-damping qubit maps and their legitimate mixtures. Using the results for image non-increasing dynamical maps, we formulate the necessary and sufficient…

We prove that a large class of expanding maps of the unit interval with a $C^2$-regular indifferent point in 0 and full increasing branches are global-local mixing. This class includes the standard Pomeau-Manneville maps $T(x) = x +…

For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…

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 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…

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 give a fairly complete characterization of the exact components of a large class of uniformly expanding Markov maps of $\mathbb{R}$. Using this result, for a class of $\mathbb{Z}$-invariant maps and finite modifications thereof, we prove…

For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way,…