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# 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 Article Yes Boyarsky, Abraham and Eslami, Peyman and Góra, Paweł and Li, Zhenyang and Meddaugh, Jonathan and Raines, Brian E. Nonlinear Dynamics 2015 10.1007/s11071-014-1802-6 980099 PAWEL GORA 25 Jun 2015 20:17 18 Jan 2018 17:50
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