In the class 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 is DC1 if F has a periodic orbit with period ≠ 2n, for any n 0. Consequently, a map in is DC1 if it has a homoclinic trajectory. This result is important since in general systems like , 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.
Strange distributionally chaotic triangular maps III / L. Paganoni, J. Smital. - In: CHAOS, SOLITONS AND FRACTALS. - ISSN 0960-0779. - 37:2(2008), pp. 517-524.
Strange distributionally chaotic triangular maps III
L. PaganoniPrimo
;
2008
Abstract
In the class 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 is DC1 if F has a periodic orbit with period ≠ 2n, for any n 0. Consequently, a map in is DC1 if it has a homoclinic trajectory. This result is important since in general systems like , 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.File | Dimensione | Formato | |
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