Minimal subshifts which display Schweizer-Smítal chaos and have zero topological entropy

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 41, Issue 1, 1998, Pages 33-38

  Liao, Gongfu ^a   Fan, Qinjie ^b  

^a JILIN UNIVERSITY   (China)

^b Siping Teachers College   (China)

Author keywords

Compact system; Minimal set; Schweizer Sm tal chaos; Subshift; Topological entropy

Indexed keywords

EID: 0002105584     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02900769     Document Type: Article

References (12)

1. Li, T. Y., Yorke, J. A., Period three implies chaos. Amer. Math. Monthly, 1975, 82: 985.
2. Schweizer, B., Smítal, J., Measures of chaos and a spectral decomposition of dynamical systems of the interval, Trans. Amer. Math. Soc., 1994, 344(2): 737.
3. Schweizer, B., Sklar, A., Probabilistic Metric Spaces, New York: North-Holland, 1983.
4. Xiong, J. C., A chaotic map with topological entropy 0, Acta Mathematics Scientia, 1986, 6: 439.
5. Liao, G. F., A note on a chaotic map with topological entropy 0, Northeastern Mathematical Journal, 1986, 2: 240.
6. Misurewicz, M., Smítal, J., Smooth chaotic maps with zero topological entropy, Erg. Th. & Dyn. Sys., 1988, 89: 421.
7. Smítal, J., Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc., 1986, 297: 269.
8. Zhou, Z. L., Weakly almost periodic points and measure centre, Science in China, Ser. A. 1993, 36(2): 142.
9. Zhou, Z. L., Liao, G. F., Wang, L. Y., The positive topological entropy not equivalent to chaos - a class of subshifts, Science in China, Ser A, 1994, 37(6): 653.
10. Gottschalk, W. H., Some remarks on almost periodic transformations, Bull. Amer. Math. Soc., 1944, 50: 915.
11. Erdös, P., Stone, A. H., Orbit-closure decompositions and almost periodic properties., Bull. Amer. Math. Soc, 1945, 51: 126.
12. Walters, P., An Introduction of Ergodic Theory, New York: Springer-Verlag, 1982.