Statistical properties of piecewise smooth hyperbolic systems in high dimensions
type: Item
instance of: scholarly article
title: Statistical properties of piecewise smooth hyperbolic systems in high dimensions
zbMATH Open document ID: 0965.37004
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: This paper deals with smooth hyperbolic systems with singularities and their SRB measures. Note that SRB measures are the only physically observable invariant measures for smooth or piecewise smooth hyperbolic dynamical systems. The author assumes that the singularities are submanifolds and proves both the existence of ergodic SRB measures and its mixing and statistical properties. The main results of this paper, however, are statistical properties -- the exponential bound on correlations and the central limit theorem.
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 37A50
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37A25
zbMATH DE Number: 1492576
zbMATH Keywords: smooth hyperbolic systems
zbMATH Keywords: singularities
zbMATH Keywords: SRB measures
zbMATH Keywords: invariant measures
zbMATH Keywords: exponential bound on correlations
zbMATH Keywords: central limit theorem
author: Nikolai Chernov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.425
OpenAlex ID: W1987210091
DOI: 10.3934/DCDS.1999.5.425
description: scientific article; zbMATH DE number 1492576