Strange distributionally chaotic triangular maps III

L. Paganoni and J. Smítal

Chaos, Solitons & Fractals, 2008, vol. 37, issue 2, 517-524

Abstract: In the class T of triangular maps of the square we consider the strongest notion of distributional chaos, DC1, originally introduced by Schweizer and Smítal [Trans Amer Math Soc 1994;344:737–854] for continuous maps of the interval. We show that a map F∈T is DC1 if F has a periodic orbit with period≠2n, for any n⩾0. Consequently, a map in T is DC1 if it has a homoclinic trajectory. This result is important since in general systems like T, positive topological entropy itself does not imply DC1. It contributes to the solution of a long-standing open problem of A. N. Sharkovsky concerning classification of triangular maps of the square.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:37:y:2008:i:2:p:517-524

DOI: 10.1016/j.chaos.2006.09.037

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