Continuity of type-I intermittency from a measure-theoretical point of view
type: Item
instance of: scholarly article
title: Continuity of type-I intermittency from a measure-theoretical point of view
zbMATH Open document ID: 0588.58052
DOI: 10.1007/BF01010987
published in: Journal of Statistical Physics
publication date: 1984-01-01T00:00:00Z
review text: We study a simple dynamical system which displays a so-called ''type-I intermittency'' bifurcation. We determine the Bowen-Ruelle measure \(\mu_{\epsilon}\) and prove that the expectation \(\mu_{\epsilon}(g)\) of any continuous function g and the Kolmogoroff-Sinai entropy \(h(\mu_{\epsilon})\) are continuous functions of the bifurcation parameter \(\epsilon\). Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 58C35
zbMATH DE Number: 3944919
zbMATH Keywords: onset of turbulence
zbMATH Keywords: dynamical systems
zbMATH Keywords: invariant measures
zbMATH Keywords: bifurcation
author: Claude Meunier
MaRDI profile type: Publication
cites work: Q5605745
cites work: CONDITIONS FOR THE ABSENCE OF PHASE TRANSITIONS IN ONE-DIMENSIONAL CLASSICAL SYSTEMS
cites work: Some properties of absolutely continuous invariant measures on an interval
full work available at URL: https://doi.org/10.1007/bf01010987
OpenAlex ID: W4301423021
description: scientific article; zbMATH DE number 3944919