Scrambled sets of continuous maps of 1-dimensional polyhedra

Transactions of the American Mathematical Society

Volumn 351, Issue 1, 1999, Pages 353-362

  Mai, Jiehua ^a  

^a SHANTOU UNIVERSITY   (China)

Author keywords

1 dimensional polyhedron; Chaos; Scrambled set; Totally chaotic map

Indexed keywords

EID: 22444455487     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02192-3     Document Type: Article

References (15)

1. LI. Alseda, J. Llibre and M. Misiurewicz, Periodic orbits of maps of Y, Trans. Amer. Math. Soc. 313(1989), 475-538. MR 90c:58145
2. Ll. Alseda and J. M. Moreno, Linear orderings and the full periodicity kernel for the n-star, J. Math. Anal. Appl. 180(1993), 599-616. MR 95e:58141
3. Ll. Alseda and X. D. Ye, No division and the set of periods for tree maps, Ergod. Th. & Dynam. Sys. 15(1995), 221-237. MR 96d:58109
4. M. A. Armstrong, Basic Topology, Springer-Verlag, New York, 1983. MR 84f:55001
5. A. Bruckner and T. Hu, On scrambled set and chaotic functions, Trans. Amer. Math. Soc. 301(1987), 289-297. MR 88f:26003
6. K. Jankova and J. Smital, A characterization of chaos, Bull. Austral. Math. Soc. 34(1986), 283-292. MR 87k:58178
7. V. Jimenez, Large chaos in smooth functions of zero topological entropy, Bull. Austral. Math. Soc. 46(1992), 271-285. MR 93h:58099
8. I. Kan, A chaotic function possessing a scrambled set of positive Lebesgue measure, Proc. Amer. Math. Soc. 92(1984), 45-49. MR 86b:26009a
9. M. Kuchta and J. Smital, Two point scrambled set implies chaos, European Conference on Iteration Theory(ECIT 87), World Sei. Publishing Co., Singapore, 1989, pp.427-430. MR 91j:58112
10. S. H. Li and X. D. Ye, Topological entropy for finite invariant subsets of Y, Trans. Amer. Math. Soc. 347(1995), 4651-4661. MR 96e:58052
11. T. Y. Li and J. Yorke, Period three implies chaos, Amer. Math. Monthly 82(1975), 985-992. MR 52:5898
12. V. J. Lopez, Paradoxical functions on the interval, Proc. Amer. Math. Soc. 120(1994), 465-473. MR 94g:58141
13. M. Misiurewicz, Chaos almost everywhere, Iteration Theory and its Functional Equations, Lecture Notes in Math., Vol.1163, Springer, Berlin, 1985, pp.125-130. MR 87e:58152
14. Z. Nitecki, Differentiate Dynamics, The M.I.T. Press, Cambridge Mass., 1971. MR 58:31210
15. J. Smital, A chaotic function with a scrambled set of positive Lebesgue measure, Proc. Amer. Math. Soc. 92(1984), 50-54. MR 86b:26009b