Sojourn times in laminar states of deterministic dynamical systems with intermittency
type: Item
instance of: scholarly article
title: Sojourn times in laminar states of deterministic dynamical systems with intermittency
zbMATH Open document ID: 0921.58036
DOI: 10.1007/BF02432337
author: K. Appert
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-06-29T00:00:00Z
review text: The author considers a kind of chaotic deterministic dynamical system, which is relevant from the stochastic viewpoint. The dynamical systems considered in this note are the iterates \(T^k\) of a mapping \(T\) from \([0,1]\) onto itself, that is \[ T(x)= \begin{cases} x+4x^2\quad & \text{for }x\in [0, \textstyle {1\over 2}],\\ x-4(1-x^2)\quad & \text{for }x\in [\textstyle {1\over 2},1]. \end{cases} \] The author investigates the behaviour of the trajectory and shows that the trajectory \(\{T^k(x)\}^n_{k=0}\) belongs to laminar states \(A\) and \(B\) for an extremely long time. The author also studies the limit of the ratio of the sojourn time of the trajectory in \(A\) to that in \(B\). The peculiarity of the dynamical systems under consideration is that they admit ergodic invariant measures.
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1289185
zbMATH Keywords: chaotic behaviour
zbMATH Keywords: laminar states
zbMATH Keywords: sojourn time
zbMATH Keywords: ergodic invariant measures
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02432337
OpenAlex ID: W1994246357
description: scientific article; zbMATH DE number 1289185