Memory loss for time-dependent piecewise expanding systems in higher dimension

Autor:	Andrei Török, Chinmaya Gupta, William Ott
Rok vydání:	2013
Předmět:	Stochastic differential equation Projected dynamical system Mixing (mathematics) Dynamical systems theory Flow (mathematics) General Mathematics Mathematical analysis Piecewise Random dynamical system Mathematics Linear dynamical system
Zdroj:	Mathematical Research Letters. 20:141-161
ISSN:	1945-001X 1073-2780
DOI:	10.4310/mrl.2013.v20.n1.a12
Popis:	We prove a counterpart of exponential decay of correlations for certain non- stationary systems. Namely, given two probability measures absolutely continuous with respect to a reference measure, their quasi-Holder distance (and in particular their L 1 distance) decreases exponentially under action by compositions of arbitrarily chosen maps close to those that are both piecewise expanding and mixing in a certain sense. This paper studies statistical properties of time-dependent dynamical systems. In such systems, the dynamical model itself is allowed to vary with time. An important example is the flow generated by a non-autonomous vector field. Perhaps the vector field depends on physical parameters that vary with time. We address memory loss for time-dependent dynamical systems, an analog of decay of correlations. The memory loss problem has been studied extensively in the contexts of stochastic differential equations (SDEs), random dynamical systems 1 , and autonomous (time
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::544489808fb0cbad384c287ebe146b38 https://doi.org/10.4310/mrl.2013.v20.n1.a12 Zobrazit plný text záznamu