arXiv subjects

Peyman Eslami

Publications and source records attributed to Peyman Eslami.

7 recordsLinked to original sources

arXiv2021

Sharp Statistical Properties for a Family of Multidimensional NonMarkovian Nonconformal Intermittent Maps

Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension, and also in higher dimensions if the map happens to be Markov. In general, the nonconformality of multidimensional intermittent maps represents a challenge that up to now is only partially addressed. We show how to prove sharp polynomial bounds on decay of correlations for a class of multidimensional intermittent maps. In addition we show that the optimal results on statistical limit laws for one-dimensional intermittent maps hold also for the maps considered here. This includes the (functional) central limit theorem and local limit theorem, Berry-Esseen estimates, large deviation estimates, convergence to stable laws and Lévy processes, and infinite measure mixing.

math.DS↗

arXiv2020

Mixing rates for symplectic almost Anosov maps

We establish sharp bounds on the mixing rates of a class of two dimensional non-uniformly hyperbolic symplectic maps. This provides a primer on how to investigate such questions in a concrete example and, at the same time, it solves a controversy between previous rigorous results and numerical experiments.

math.DS↗

arXiv2020

Inducing schemes for multi-dimensional piecewise expanding maps

We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical properties of dynamical systems with some hyperbolicity.

math.DS↗

arXiv2019

On piecewise expanding maps

We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also provide sufficient conditions for the existence of inducing schemes where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures can then be used to deduce finer statistical properties.

math.DS↗

arXiv2014

Exponential Mixing for Skew Products with Discontinuities

We consider the skew product $F: (x,u) \mapsto (f(x), u + τ(x))$, where the base map $f : \mathbb{T}^{1} \to \mathbb{T}^{1}$ is piecewise $\mathcal{C}^{2}$, covering and uniformly expanding, and the fibre map $τ: \mathbb{T}^{1} \to \mathbb{R}$ is piecewise $\mathcal{C}^{2}$. We show the dichotomy that either this system mixes exponentially or $τ$ is cohomologous (via a Lipschitz function) to a piecewise constant.

math.DS↗

arXiv2014

Stretched-exponential mixing for $\mathscr{C}^{1+α}$ skew products with discontinuities

Consider the skew product $F:\mathbb{T}^2 \to \mathbb{T}^2$, $F(x,y)= (f(x),y+τ(x))$, where $f:\mathbb{T}^1\to \mathbb{T}^1$ is a piecewise $\mathscr{C}^{1+α}$ expanding map on a countable partition and $τ:\mathbb{T}^1 \to \mathbb{R}$ is piecewise $\mathscr{C}^1$. It is shown that if $τ$ is not Lipschitz-cohomologous to a piecewise constant function on the joint partition of $τ$ and $f$, then $F$ is mixing at a stretched-exponential rate.

math.DS↗

arXiv2011

Eventually Expanding Maps

In this paper we show that the piecewise linear map f(x) = px for x in [0,1/p], and sx-s/p for x in (1/p,1], p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding and exact.

math.DS↗