Properties of fully developed chaos in one-dimensional maps
type: Item
instance of: scholarly article
title: Properties of fully developed chaos in one-dimensional maps
zbMATH Open document ID: 0587.58029
DOI: 10.1007/BF01018554
author: P. Szépfalusy
author: Géza Györgyi
published in: Journal of Statistical Physics
publication date: 1984-01-01T00:00:00Z
review text: We consider single-humped symmetric one-dimensional maps generating fully developed chaotic iterations specified by the property that on the attractor the mapping is everywhere two to one. To calculate the probability distribution function, and in turn the Lyapunov exponent and the correlation function, a perturbation expansion is developed for the invariant measure. Besides deriving some general results, we treat several examples in detail and compare our theoretical results with recent numerical ones. Furthermore, a necessary condition is deduced for the probability distribution function to be symmetric and an effective functional iteration method for the measure is introduced for numerical purposes.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 3942554
zbMATH Keywords: chaos
zbMATH Keywords: probability distribution
zbMATH Keywords: perturbation theory
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: correlation function
MaRDI profile type: Publication
cites work: Q3908199
cites work: Chaos and order in nature. Proceedings of the International Symposium on Synergetics at Schloß Elmau, Bavaria, April 27 - May 2, 1981
cites work: Dynamical systems and chaos. Proceedings of the Sitges Conference on Statistical Mechanics, Sitges, Barcelona/Spain, September 5-11, 1982
cites work: Applications conservant une mesure absolument continue par rapport à \(dx\) sur \([0,1]\)
cites work: Period-doubling bifurcations and associated universal properties including parameter dependence.
cites work: Statistical mechanics of deterministic chaos. The case of one-dimensional discrete process.
cites work: On unimodal linear transformations and chaos. I
cites work: Quantitative universality for a class of nonlinear transformations
full work available at URL: https://doi.org/10.1007/bf01018554
OpenAlex ID: W204848748
description: scientific article; zbMATH DE number 3942554