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. Paganoni
Primo
;
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.
Triangular maps; Distributional chaos; Homoclinic trajectory
Settore MAT/05 - Analisi Matematica
Article (author)
File in questo prodotto:
File Dimensione Formato  
Strange distributionally triangular maps III.pdf

accesso aperto

Tipologia: Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione 204.19 kB
Formato Adobe PDF
204.19 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/27522
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 6
social impact