Weakly attracting repellors for piecewise convex maps
type: Item
instance of: scholarly article
title: Weakly attracting repellors for piecewise convex maps
zbMATH Open document ID: 0772.58036
DOI: 10.1007/BF03167275
author: Tomoki Inoue
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1993-02-16T00:00:00Z
review text: The author introduces the notion of a ``weakly attracting repellor'' which is an unstable fixed point such that the trajectories stay in its neighborhood for an extremely long time. He studies a class of piecewise convex increasing maps which includes some intermittent dynamical systems and a class of cusp type maps which is related to the Lorenz equation with a critical parameter. He also proves that if piecewise convex maps have weak attracting repellors under some condition the Lyapunov number is 0 for almost every point. The proofs use a specially defined \(\sigma\)- finite invariant measure.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 109307
zbMATH Keywords: weakly attracting repellor
zbMATH Keywords: unstable fixed point
reviewed by: Ubiratan D'Ambrosio
MaRDI profile type: Publication
cites work: Absolutely continuous invariant measures for maps with flat tops
cites work: Asymptotic stability of densities for piecewise convex maps
cites work: Ratio ergodic theorems for maps with indifferent fixed points
cites work: Asymptotic periodicity of densities and ergodic properties for nonsingular systems
cites work: Globally asymptotic properties of proliferating cell populations
cites work: Exact Dynamical Systems and the Frobenius-Perron Operator
cites work: On the concept of attractor
cites work: First return map and invariant measures
cites work: Expanding Maps on Sets Which are Almost Invariant: Decay and Chaos
cites work: Estimates of the invariant densities of endomorphisms with indifferent fixed points
cites work: Transformations on [0,1] with infinite invariant measures
cites work: Q3931654
full work available at URL: https://doi.org/10.1007/bf03167275
OpenAlex ID: W2047780754
description: scientific article; zbMATH DE number 109307