Necessary and sufficient conditions for semi-uniform ergodic theorems and their applications

Discrete and Continuous Dynamical Systems

Volumn 14, Issue 3, 2006, Pages 409-417

  Zheng, Zuohuan ^a   Xia, Jing ^b   Zheng, Zhiming ^b,c  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b PEKING UNIVERSITY   (China)

^c BEIHANG UNIVERSITY   (China)

Author keywords

Ergodic theorems; Quasiperiodically forced systems; Strange attractors

Indexed keywords

EID: 33644519984     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2006.14.409     Document Type: Article

References (19)

1. L. Arnold, Random Dynamical Systems, Berlin: Springer, (1998)
2. G. Chen, and G. Ueta, Yet another chaotic attractor, Int.J.of Bifurcation and Chaos 9 (1999) 1465-1466.
3. C. Conley, Isolated Invariant Set and the Morse Index, CBMS Regional Conf.Ser.in Math. No.38(1978).
4. U. Fendel, J. Kurths, and A. Pikovsky, Strange non-chaotic attactor in a quasiperiodically forced circle map, Physica D 88 (1995) 176-186.
5. C. Grebogi, E. Ott, S. Pelikan, and J.A. Yorke, Strange attractors that are not chaotic, Physica D 13(1984) 261-268.
6. M.R. Herman, Une méthode pour minorer les exposants de Lyapunov et quelques examples moutrant le caractére local d'um théorè me d'Arnold et de Moser sur le tore de dimension 2, Comment. Math. Helv. 58(1983) 453-502.
7. B.R. Hunt, and E. Ott, Optimal periodic orbits of chaotic systems, Phys. Rev. 76 (1996) 2254-2257.
8. B.R. Hunt, and E. Ott, Optimal periodic orbits of chaotic systems occur at low period, Phys. Rev. E 54 (1996) 328-337.
9. A. Katok, and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge: Cambridge University Press, (1995).
10. G. Keller, A note on strange nonchaotic attractors, Fund.math. 151(1996) 139-148.
11. J.C. Oxtoby, Ergodic Sets, Bull. AMS 58(1952) 116-136.
12. J. Stark, Invariant graphs for forced systems, Physica D 109 (1997) 163-179.
13. R. Sturman, and J. Stark, Semi-uniform ergodic theorem and applications to forced systems, Nonlinearity 13(2000) 113-143.
14. G.C. Yuan, and B.R. Hunt, Optimal orbits of axiom A systems, Nonlinearity 12 (1999) 1207-1224.
15. Z. Zheng,Generalized ergodicity, Science in China 44 (2001) 1098-1106.
16. G. Blé, External arguments and invariant measures for the quadratic family, Disc. Cont. Dynam. Systems 11 (2004) 241-260.
17. X. Bressaud, Expanding interval maps with intermittent behaviour, physical measures and time scales Disc. Cont. Dynam. Systems 11 (2004) 517-546.
18. M. Pivato, Invariant measures for bipermutative cellular automata, Disc. Cont. Dynam. Systems 12 (2005) 723-736.
19. L. Barreira, Lyapunov exponents for continuous transformations and dimension theroy, Disc. Cont. Dynam. Systems 13 (2005) 469-490.