Variational principles and mixed multifractal spectra

Transactions of the American Mathematical Society

Volumn 353, Issue 10, 2001, Pages 3919-3944

  Barreira, L ^a   Saussol, B ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Dimension spectrum; Entropy spectrum; Variational principle

Indexed keywords

EID: 23044530336     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-01-02844-6     Document Type: Article

References (12)

1. L. Barreira, A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems, Ergodic Theory Dynam. Systems 16 (1996), 871-927. MR 98a:58124
2. L. Barreira, Ya. Pesin and J. Schmeling, Dimension and product structure of hyperbolic measures, Ann. of Math. (2) 149 (1999), 755-783. MR 2000f:37027
3. L. Barreira and J. Schmeling, Sets of "non-typical" points have full topological entropy and full Hausdorff dimension, Israel J. Math. 116 (2000), 29-70. CMP 2000:13
4. R. Bowen, Some systems with unique equilibrium states, Math. Systems Theory 8 (1975), 193-202. MR 53:3257
5. G. Keller, Equilibrium states in ergodic theory, London Mathematical Society Student Texts 42, Cambridge University Press, 1998. MR 99e:28022
6. E. Olivier, Analyse multifractale de fonctions continues, C. R. Acad. Sci. Paris 326 (1998), 1171-1174. MR 99h:58109
7. Ya. Pesin, Dimension theory in dynamical systems: contemporary views and applications, Chicago Lectures in Mathematics, Chicago University Press, 1997. MR 99b:58003
8. D. Ruelle, Thermodynamic formalism, Encyclopedia of mathematics and its applications, vol. 5, Addison-Wesley, 1978. MR 80g:82017
9. J. Schmeling, Symbolic dynamics for β-shifts and self-normal numbers, Ergodic Theory Dynam. Systems 17 (1997), 675-694. MR 98e:11080
10. J. Schmeling, Entropy preservation under Markov coding, preprint.
11. F. Takens and E. Verbitski, On the variational principle for the topological entropy of certain non-compact sets, preprint.
12. P. Walters, Equilibrium states for β-transformations and related transformations, Math. Z. 159 (1978), 65-88. MR 57:6370