Multifractal formalism for some parabolic maps

Ergodic Theory and Dynamical Systems

Volumn 20, Issue 3, 2000, Pages 843-857

  Nakaishi, Kentaro ^a  

^a UNIVERSITY OF TOKYO   (Japan)

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[No Author keywords available]

Indexed keywords

EID: 0040953087     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385700000456     Document Type: Article

References (23)

1. J. Aaronson. An Introduction to Infinite Ergodic Theory (Mathematical Surveys and Monographs, 50). American Mathematical Society, 1997
2. J. Aaronson, M. Denker and M. Urbański. Ergodic theory for Markov fibred systems and parabolic rational maps. Trans. Amer. Math. Soc. 337 (1993), 495-548.
3. V. Baladi and G. Keller. Zeta functions and transfer operators for piecewise monotone transformation. Commun. Math. Phys. 127 (1990), 459-477.
4. R. Bowen. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms (Lecture Notes in Mathematics, 470). Springer, 1975.
5. R. Bowen. Invariant measures for Markov maps of the interval. Commun. Math. Phys. 69 (1979), 1-17.
6. P. Collet and P. Ferrero. Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point. Ann. Inst. Henri Poincaré 52 (1990), 283-301.
7. M. Denker and M. Urbański. Absolutely continuous invariant measures for expansive rational maps with rationally indifferent periodic points. Forum Math. 3 (1991), 561-579.
8. M. Feigenbaum. Presentation functions, fixed points, and a theory of scaling function dynamics. J. Stat. Phys. 52 (1988), 527-569.
9. T. Kato. Perturbation Theory for Linear Operators. Springer, Berlin, 1976.
10. A. Lopes. The dimension spectrum of maximal measure. SIAM J. Math. Anal. 20 (1989), 1243-1254.
11. M. Misiurewicz and W. Szlenk. Entropy of piecewise monotone mappings. Studia Math. 67 (1980), 45-63.
12. W. Parry and M. Pollicott. Zeta functions and the periodic orbit structure of hyperbolic dynamics. Asterisque 187-188 (1990).
13. Y. Pesin and H. Weiss. A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions. J. Stat. Phys. 86 (1997), 233-275.
14. Y. Pesin and H. Weiss. The multifractal analysis of Gibbs measures: motivation, mathematical foundation and examples. Chaos 7 (1997), 89-106.
15. M. Pollicott and H. Weiss. Multifractal analysis of Lyapunov exponent for continued fraction and Manneville-Pomeau transformations and applications to Diophantine approximation. Commun. Math. Phys. 207 (1999), 145-171.
16. T. Prellberg and J. Slawny. Maps of intervals with indifferent fixed points; thermodynamic formalism and phase transitions. J. Stat. Phys. 66 (1992), 503-514.
17. D. Ruelle. Repellers for real analytic maps. Ergod. Th. & Dynam. Sys. 2 (1982), 99-107.
18. D. Ruelle. The thermodynamic formalism for expanding maps. Commun. Math. Phys. 125 (1989), 239-262.
19. D. Ruelle. Spectral properties of a class of operators associated with maps in one dimension. Ergod. Th. & Dynam. Sys. 11 (1991), 757-767.
20. F. Schweiger. Numbertheoretical endomorphisms with σ-finite invariant measure. Israel J. Math. 21 (1975), 308-318.
21. M. Thaler. Transformations on [0, 1] with infinite invariant measures. Israel J. Math. 46 (1983), 67-96.
22. P. Walters. Invariant measures and equilibrium states for some mappings which expand distances. Trans. Amer. Math. Soc. 236 (1978), 121-153.
23. M. Yuri. On the convergence to equilibrium states for certain non-hyperbolic systems. Ergod. Th. & Dynam. Sys. 17 (1997), 977-1000.