Chaos and Entropy for Circle Maps

Tokyo Journal of Mathematics

Volumn 25, Issue 2, 2002, Pages 453-458

  Miyazawa, Megumi ^a  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27644597920     PISSN: 03873870     EISSN: None     Source Type: Journal    
DOI: 10.3836/tjm/1244208864     Document Type: Article

References (17)

1. L. ALSEDÀ, J. LLIBRE and M. MISIUREWICZ, Combinatorial dynamics and entropy in dimension one, Advanced Series in Nonlinear Dynamics 5 (1993), World Scientific.
2. J. BANKS, J. BROOKS, G. CAIRNS, G. DAVIS and P. STACEY, On Devaney’s definition of chaos, Amer. Math. Monthly 99 (1992), 332–334.
3. L. S. BLOCK and W. A. COPPEL, Dynamics in one dimension, Lecture Notes in Mathematics 1513 (1992), Springer.
4. L. BLOCK, E. COVEN, I. MULVEY and Z. NITECKI, Homoclinic and non-wandering points for maps of the circle, Ergod. Th. and Dynam. Sys. 3 (1983), 521–532.
5. R. L. DEVANEY, An introduction to chaotic dynamical systems, Benjamin/Cummings (1986).
6. E. GLASNER and B. WEISS, Sensitive dependence on initial conditions, Nonlinearity 6 (1993), 1067–1075.
7. R. ITO, Rotation sets are closed, Math. Proc. Cambridge Philos. Soc. 89 (1981), 107–111.
8. M. KUCHTA, Characterization of chaos for continuous maps of the circle, Comment. Math. Univ. Carolin. 31 (1990), 383–390.
9. S. LI, Dynamical properties of the shift maps on the inverse limit spaces, Ergod. Th. and Dynam. Sys. 12 (1992), 95–108.
10. S. LI, ω-chaos and topological entropy, Trans. Amer. Math. Soc. 339 (1993), 243–249.
11. T.-Y. LI and J. A. YORKE, Period three implies chaos, Amer. Math. Monthly 82 (1975), 985–992.
12. M. MISIUREWICZ, Twist sets for maps of the circle, Ergod. Th. and Dynam. Sys. 4 (1984), 391–404.
13. S. SILVERMAN, On maps with dense orbits and the definition of chaos, Rocky Mountain J. Math. 22 (1992), 353–375.
14. J. SMÍTAL, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), 269–282.
15. M. VELLEKOOP and R. BERGLUND, On intervals, transitivity = chaos, Amer. Math. Monthly 101 (1994), 353–355.
16. J. XIONG, The attracting centre of a continuous self-map of the interval, Ergod. Th. and Dynam. Sys. 8, (1988), 205–213.
17. J. XIONG and Z. YANG, Chaos caused by a topologically mixing map, Dynamical systems and related topics (Nagoya, 1990), Adv. Ser. Dynam. Systems, 9 World Sci. (1991), 550–572.