Statistics of strange attractors by generalized cell mapping
type: Item
instance of: scholarly article
title: Statistics of strange attractors by generalized cell mapping
zbMATH Open document ID: 0624.58023
DOI: 10.1007/BF01010488
author: Chieh-Su Hsu
author: Myun C. Kim
published in: Journal of Statistical Physics
publication date: 1985-01-01T00:00:00Z
review text: It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration are also made.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 62P99
zbMATH DE Number: 4013586
zbMATH Keywords: statistical properties of strange attractors
zbMATH Keywords: generalized cell mapping
zbMATH Keywords: nonlinear dynamical systems
zbMATH Keywords: Hénon-Pomeau map
zbMATH Keywords: Zaslavskij map
zbMATH Keywords: forced Duffing system
zbMATH Keywords: cell-to-cell mapping
zbMATH Keywords: invariant distribution
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01010488
OpenAlex ID: W2075632853
description: scientific article; zbMATH DE number 4013586