Recurrence, dimension and entropy

Journal of the London Mathematical Society

Volumn 64, Issue 1, 2001, Pages 229-244

  Fan, Ai Hua ^a   Feng, De Jun ^c   Wu, Jun ^b  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b WUHAN UNIVERSITY   (China)

^c TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000434272     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0024610701002137     Document Type: Article

References (23)

1. L. BARREIRA and J. SCHMELING, 'Invariant sets with zero measure and full Hausdorff dimension', AMS Electronic Research Announcements 3 (1997) 114-118.
2. T. BOUSCH, 'Le poisson n'a pas d'arêtes', Ann. Inst. H. Poincaré, to appear.
3. R. BOWEN, "Topological entropy for noncompact sets', Trans. Amer. Math. Soc. 184 (1973) 125-136.
4. R. BOWEN, 'Equilibrium states and the ergodic theory of Anosov diffeomorphisms', Lecture Notes in Mathematics 470 (Springer, 1975).
5. M. BRIN and A. KATOK, 'On local entropy', Geometric Dynamics, Rio de Janeiro, 1981, Lecture Notes in Mathematics 1007 (Springer, Berlin, 1983) 30-38.
6. S. BULLETT and P. SENTENAC, 'Ordered orbits of the shift, square roots, and the devil's staircase', Math. Proc. Cambridge Philos. Soc. 115 (1994) 451-481.
7. J. L. DOOB, Stochastic processes (John Wiley, New York, 1953).
8. K. J. FALCONER, Fractal geometry: mathematical foundation and applications (John Wiley, New York, 1990).
9. A. H. FAN, 'Sur les dimensions de mesures', Studio Math. 111 (1994) 1-17.
10. A. H. FAN and D. J. FENG, 'On the distribution of long-term time average on the symbolic space', J. Statist. Phys. 99 (2000) 813-856 (see also 'Analyse multifractale de la récurrence sur l'espace symbolique', C. R. Acad. Sci. Paris Sér. I Math. (1998) 629-632).
11. A. H. FAN and D. J. FENG, 'On the distribution of long-term time average on the symbolic space', J. Statist. Phys. 99 (2000) 813-856 (see also 'Analyse multifractale de la récurrence sur l'espace symbolique', C. R. Acad. Sci. Paris Sér. I Math. (1998) 629-632).
12. D. J. FENG, H. RAO and J. WU, 'The net measure properties of symmetric Cantor sets and their applications', Progr. Natur. Sci. 7 (1997) 172-178.
13. D. J. FENG, Z. Y. WEN and J. WU, 'Some dimensional results for homogeneous Moran sets', Sci. China Ser. A 40 (1997) 475-482.
14. O. JENKINSON, 'Conjugacy rigidity, cohomological triviality and barycentres of invariant measures', PhD Thesis, Warwick University, 1996.
15. O. JENKINSON, 'Geometric barycentres of invariant measures for circle maps', Ergodic Theory Dynam. Systems, to appear.
16. J. P. KAHANE, Some series of random functions (Cambridge University Press, 1985).
17. R. MAÑE, 'Generic properties and problems of minimizing measures of Lagrangian systems', Nonlinearity 9 (1996) 273-310.
18. P. MATTILA, Geometry of sets and measures in Euclidean spaces, fractals and rectifiability (Cambridge University Press, 1995).
19. Y. PESIN and B. PITSKEL, 'Topological pressure and the variational principle for non-compact sets', Fund. Anal. Appl. 18 (1984) 307-318.
20. K. PETERSON, Ergodic theory (Cambridge University Press, 1983).
21. R. T. ROCKAFELLAR, Convex analysis (Princeton University Press, 1970).
22. D. RUELLE, 'Thermodynamic formalism: the mathematical structures of classical equilibrium statistical mechanics', Encyclopedia of Mathematics and its Applications-Vol. 5 (Addison Wesley, 1978).
23. P. WALTERS, An introduction to ergodic theory (Springer, Berlin, 1982).