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Chaos for successive maxima map implies chaos for the original map

Title:

Chaos for successive maxima map implies chaos for the original map

Boyarsky, Abraham, Eslami, Peyman, Góra, Paweł, Li, Zhenyang, Meddaugh, Jonathan and Raines, Brian E. (2015) Chaos for successive maxima map implies chaos for the original map. Nonlinear Dynamics, 79 (3). pp. 2165-2175. ISSN 0924-090X

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Official URL: http://dx.doi.org/10.1007/s11071-014-1802-6

Abstract

$\tau$ is a continuous map on a metric compact space $X$. For a continuous function $\phi:X\to\mathbb R$ we considera 1-dimensional map $T$ (possibly multi-valued) which sends a local $\phi$-maximum on $\tau$ trajectory to the next one: consecutive maxima map. The idea originated with famous Lorenz's paper on strange attractor. We prove that if $T$ has a horseshoe disjoint from fixed points, then $\tau$ is in some sense chaotic, i.e., it has a turbulent trajectory and thus a continuous invariant measure.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Refereed:Yes
Authors:Boyarsky, Abraham and Eslami, Peyman and Góra, Paweł and Li, Zhenyang and Meddaugh, Jonathan and Raines, Brian E.
Journal or Publication:Nonlinear Dynamics
Date:2015
Digital Object Identifier (DOI):10.1007/s11071-014-1802-6
ID Code:980099
Deposited By: PAWEL GORA
Deposited On:25 Jun 2015 20:17
Last Modified:18 Jan 2018 17:50
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