On Li-Yorke pairs

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 547, 2002, Pages 51-68

  Blanchard, François ^a   Glasner, Eli ^b   Kolyada, Sergiǐ ^c   Maass, Alejandro ^d  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b TEL AVIV UNIVERSITY   (Israel)

^c INSTITUTE OF HYDROBIOLOGY   (Ukraine)

^d UNIVERSITY OF CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036258654     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2002.053     Document Type: Article

References (33)

1. E. Akin, Personal communication.
2. E. Akin, J. Auslander and K. Berg, When is a transitive map chaotic?, Convergence in ergodic theory and probability (Columbus, OH, 1993), vol. 5, Ohio State Univ. Math. Res. Inst. Publ., de Gruyter, Berlin (1996), 25-40.
3. E. Akin and S. Glasner, Residual properties and almost equicontinuity, J. Anal. Math., to appear.
4. J. Auslander, Minimal flows and their extensions, North-Holland Math. Stud. 153, Amsterdam 1988.
5. J. Auslander and J. Yorke, Interval maps, factors of maps and chaos, Tohoku Math. J. 32 (1980), 177-188.
6. F. Blanchard, E. Glasner and B. Host, A variation on the variational principle and applications to entropy pairs, Erg. Th. Dynam. Sys. 17 (1997), 29-43.
7. F. Blanchard, B. Host and A. Maass, Topological complexity, Erg. Th. Dynam. Sys. 20 (2000), 641-662.
8. F. Blanchard, B. Host and S. Ruette, Asymptotic pairs in positive-entropy systems, Erg. Th. Dynam. Sys., to appear.
9. I. U. Bronstein, Extensions of minimal transformation groups (translated from the Russian), Martinus Nijhoff Publishers, The Hague 1979.
10. M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Springer Lect. Notes Math. 527, Berlin 1976.
11. R. Devaney, Chaotic dynamical systems, 2d edn., Addison-Wesley, New York 1989.
12. R. Ellis, S. Glasner and L. Shapiro, Proximal-isometric flows, Adv. Math. 17 (1975), 213-260.
13. X. Fu, Y. Fu, J. Duan and R. S. MacKay, Chaotic properties of subshifts generated by a non-periodic recurrent orbit, Int. J. Bif. Chaos 10 (2000), 1067-1073.
14. H. Furstenberg, Disjointness in ergodic theory, minimal sets and a problem in diophantine approximation, Math. Sys. Th. 1 (1967), 1-55.
15. H. Furstenberg, The structure of distal flows, Amer. J. Math. 85 (1963), 477-515.
16. E. Glasner, A simple characterization of the set of μ-entropy pairs and applications, Israel J. Math. 102 (1997), 13-27.
17. E. Glasner, Proximal flows, Springer Lect. Notes Math. 517 (1976).
18. S. Glasner and D. Maon, Rigidity in topological dynamics, Erg. Th. Dynam. Sys. 9 (1989), 309-320.
19. E. Glasner and B. Weiss, Sensitive dependence on initial conditions, Nonlin. 6 (1993), 1067-1075.
20. W. Huang and XD. Ye, Homeomorphisms with the whole compacta being scrambled sets, Erg. Th. Dynam. Sys., to appear.
21. W. Huang and XD. Ye, Devaney's chaos or 2-scattering implies Li-Yorke chaos, Topol. Appl., to appear.
22. A. Iwanik, Independent sets of transitive points, Dynam. Sys. Erg. Th. 23. Banach Center Publications (1989), 277-282.
23. S. Kolyada and L'. Snoha, Some aspects of topological transitivity - a survey, Grazer Math. Ber. 334 (1997), 3-35.
24. S. Kolyada, L'. Snoha and S. Trofimchuk, Noninvertible minimal maps, Fund. Math., to appear.
25. M. Kuchta and J. Smítal, Two point scrambled set implies chaos, European Conference on Iteration Theory (ECIT 87), World Sci. Publishing, Singapore (1989), 427-430.
26. K. Kuratowski, Applications of the Baire-category method to the problem of independent sets, Fund. Math. 81 (1973), 65-72.
27. T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Month. 82 (1975), 985-992.
28. J. Mycielski, Independent sets in topological algebras, Fund. Math. 55 (1964), 139-147.
29. J. C. Oxtoby, Measure and category, Springer-Verlag, 1980.
30. M. Rees, A point distal transformation of the torus, Israel J. Math. 32 (1979), 201-208.
31. J. Xiong and Z. Yang, Chaos caused by a topologically mixing map, Adv. Ser. Dyn. Sys. 9, World Scientific (1990), 550-572.
32. R. J. Zimmer, Extensions of ergodic group actions, Ill. J. Math. 20 (1976), 373-409.
33. R. J. Zimmer, Extensions of ergodic actions and generalized discrete spectrum, Ill. J. Math. 20 (1976), 555-588.