General multifractal analysis of local entropies

Fundamenta Mathematicae

Volumn 165, Issue 3, 2000, Pages 203-237

  Takens, Floris ^a   Verbitski, Evgeny ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001287913     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. L. Barreira, Ya. Pesin, and J. Schmeling, Multifractal spectra and multifractal rigidity for horseshoes, J. Dynam. Control Systems 3 (1997), 33-49.
2. _, _, _, On a general concept of multifractality: multifractal spectra for dimensions, entropies, and Lyapunov exponents. Multifractal rigidity, Chaos 7 (1997), 27-38.
3. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems, Cambridge Univ. Press, Cambridge, 1993.
4. R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc. 184 (1973), 125-136.
5. _, Some systems with unique equilibrium states, Math. Systems Theory 8 (1974/75), 193-202.
6. M. Brin and A. Katok, On local entropy, in: Geometric Dynamics (Rio de Janeiro, 1981), Lecture Notes in Math. 1007, Springer, Berlin, 1983, 30-38.
7. K. Falconer, Fractal Geometry, Wiley, Chichester, 1990.
8. P. Grassberger and I. Procaccia, Dimensions and entropies of strange attractors from a fluctuating dynamics approach, Phys. D 13 (1984), 34-54.
9. M. Guysinsky and S. Yaskolko, Coincidence of various dimensions associated with metrics and measures on metric spaces, Discrete Contin. Dynam. Systems 3 (1997), 591-603.
10. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Fractal measures and their singularities: the characterization of strange sets, Phys. Rev. A (3), 33 (1986), 1141-1151.
11. N. T. A. Haydn and D. Ruelle, Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification, Comm. Math. Phys. 148 (1992), 155-167.
12. H. Hu, Decay of correlations for piecewise smooth maps with indifferent fixed points, preprint, 1998.
13. S. Isola, Dynamical zeta functions and correlation functions for non-uniformly hyperbolic transformations, preprint, 1995.
14. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia Math. Appl. 54, Cambridge Univ. Press, Cambridge, 1995.
15. C. Liverani, B. Saussol, and S. Vaienti, A probabilistic approach to intermittency, preprint.
16. L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), 82-196.
17. Ya. B. Pesin, Dimension Theory in Dynamical Systems, Univ. of Chicago Press, Chicago, IL, 1997.
18. Ya. B. Pesin and B. S. Pitskel', Topological pressure and the variational principle for noncompact sets, Funktsional. Anal. i Prilozhen. 18 (1984), no. 4, 50-63 (in Russian).
19. G. Pianigiani, First return map and invariant measures, Israel J. Math. 35 (1980), 32-48.
20. T. Prellberg and J. Slawny, Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions, J. Statist. Phys. 66 (1992), 503-514.
21. A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, New York, 1973.
22. J. Schmeling, On the completeness of multifractal spectra, preprint WIAS, Berlin, 1996.
23. F. Takens and E. Verbitski, Generalized entropies: Rényi and correlation integral approach, Nonlinearity 11 (1998), 771-782.
24. _, _, Multifractal analysis of local entropies for expansive homeomorphisms with specification, Comm. Math. Phys. 203 (1999), 593-612.
25. M. Urbański, Parabolic Cantor sets, Fund. Math. 151 (1996), 241-277.
26. T. Ward, Entropy of Compact Group Automorphisms, lecture notes, 1994.
27. L.-S. Young, Recurrence times and rates of mixing, preprint, 1997.
28. M. Yuri, Thermodynamic formalism for certain nonhyperbolic maps, preprint.