Li and Yorke chaos with respect to the cardinality of the scrambled sets

Chaos, Solitons and Fractals

Volumn 24, Issue 5, 2005, Pages 1203-1206

  Guirao, Juan Luis García ^a   Lampart, Marek ^b  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

^b SILESIAN UNIVERSITY IN OPAVA   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; CONFORMAL MAPPING; SET THEORY; THEOREM PROVING; TOPOLOGY;

CANTOR SET; LI-YORKE CHAOS; SCAMBLED SETS;

CHAOS THEORY;

EID: 13444310844     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2004.09.103     Document Type: Article

References (11)

1. Barrio A, García JL, Jiménez V, Looking for the smallest notion of chaos in discrete dynamical systems, Preprint 2004
2. Blanchard F, Durand F, Maas A. constant-length substitutions and countable scrambled sets, Preprint 2003
3. F. Blanchard, E. Glasner, S. Kolyada, and A. Maas On Li-Yorke pairs J. Reine Angew. Math. 547 2002 51 68
4. G.L. Forti, L. Paganoni, and J. Smítal Strange triangular maps of the square Bull. Aust. Math. Soc. 51 1995 398 415
5. J. Hocking, and G. Young Topology 1988 Addison-Wesley
6. W. Huang, and X. Ye Homeomorphisms with the whole compacts being scrambled sets Erg. Th. Dynam. Sys. 21 2001 77 91
7. B.P. Kitchens Symbolic dynamics, one-sided, two-sided and countable state Markov shifts 1998 Springer Berlin
8. M. Kuchta Characterization of chaos for continuous maps of the circle Commentat. Math. Univ. Carol. 31 2 1990 383 390
9. Kuchta M, Smítal J. Two point scrambled set implies chaos, Proc Eur Conf on Iteration Theory, Spain 1987. Singapore: World Scientific; 1989; pp. 427-430
10. M. Lampart Two kinds of chaos and relations between them Acta Math. Univ. Comenianae LXXII 1 2003 119 127
11. T.Y. Li, and J.A. Yorke Period three implies chaos Amer. Math. Monthly 82 1975 985 992