A bound for the rate of decrease of correlation in one-dimensional dynamical systems
type: Item
instance of: scholarly article
title: A bound for the rate of decrease of correlation in one-dimensional dynamical systems
zbMATH Open document ID: 0549.28024
DOI: 10.1007/BF01076363
author: M. L. Blank
publication date: 1984-01-01T00:00:00Z
review text: Let T be a mapping of [0,1] into itself such that there exists a finite partition \(0=a_ 0<a_ 1<...<a_ k=1\) for which T is monotone and of class \(C^ 1\) on each \((a_{i-1},a_ i)\), the function 1/\(| T'|\) is of bounded variation on each \([a_{i-1},a_ i]\) and \(\inf_{x}| T'(x)| >1.\) Then T is known to have an invariant measure \(\mu\) absolutely continuous with respect to Lebesgue measure. For \(f,g\in C^ 1[0,1]\) the n-th correlation is defined by \[ K_ n(f,g)=\int f(T^ nx)g(x)d\mu -\int f(x)d\mu\int g(x)d\mu. \] The author investigates the rate of decrease of \(K_ n(f,g)\) for mixings T.
Mathematics Subject Classification ID: 28D10
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 3875613
zbMATH Keywords: bounded variation
zbMATH Keywords: invariant measure
zbMATH Keywords: absolutely continuous
zbMATH Keywords: n-th correlation
MaRDI profile type: Publication
cites work: Ergodic properties of invariant measures for piecewise monotonic transformations
Recommended article: Absolutely continuous invariant measures for non-uniformly expanding maps
Recommended article: Decay of correlations for weakly expansive dynamical systems
Recommended article: Decay of correlations in one-dimensional dynamics
Recommended article: Quenched decay of correlations for one-dimensional random Lorenz maps
Recommended article: Q4285532
Recommended article: Decay of correlations for nonuniformly expanding systems
Recommended article: Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenz-like maps
Recommended article: Q4786850
Recommended article: Q4541942
Recommended article: Exponential decay of correlations for a real-valued dynamical system generated by a \(k\) dimensional system
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3875613