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  Far East Journal of Dynamical Systems  
 ISSN: 0972-1118
 
 
 

     Far East Journal of Dynamical Systems
    Volume 11, Issue 1, Pages 1 - 16 (February 2009)


ESTIMATES OF LARGE DEVIATIONS IN DYNAMICAL SYSTEMS BY A NON-ADDITIVE THERMODYNAMIC FORMALISM

Alejandro Mesón (Argentina) and Fernando Vericat (Argentina)

Received October 2, 2006

References:



[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.

[2] R. E. Bowen, Periodic points and measures for Axiom-A diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971), 377-397.

[3] R. Bowen, Topological entropy for non-compact sets, Trans. Amer. Math. Soc. 184 (1973), 125-136.

[4] R. Ellis, Large deviations for a general class of random vectors, Ann. Prob. 12 (1984), 1-12.

[5] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge Univ. Press, 1995.

[6] G. Keller, Equilibrium States in Ergodic Theory, London Math. Soc. Studies Texts 42, Cambridge Univ. Press, 1998.

[7] Y. Kifer, Large deviations in dynamical systems and stocastic processes, Trans. Amer. Math. Soc. 321(2) (1990), 503-524.

[8] A. M. Mesón and F. Vericat, Dimension theory and Fuchsian groups, Acta Appl. Math. 80 (2004), 95-121.

[9] Y. Pesin, Dimension Theory in Dynamical Systems, Contemporary Views and Applications, The University of Chicago Press, Chicago, 1997.

[10] Y. Pesin and B. Pitskel’, Topological pressure and the variational principle for noncompact sets, Funktsional Anal. i. Prilozhen 18 (1984), 50-63.

[11] D. Ruelle, Thermodynamic Formalism, Encyclopedia of Mathematics and its Applications, Addison-Wesley, 1978.

[12] J. Schmeling, Symbolic dynamics for -shifts and self-normal numbers, Ergodic Theory Dynam. Systems 17 (1998), 771-782.

[13] F. Takens and E. Verbitski, Multifractal analysis of local entropies for expansive homeomorphisms with specification, Commun. Math. Phys. 203 (1999), 593-612.

[14] L. S. Young, Some large deviations results for dynamical systems, Trans. Amer. Math. Soc. 318 (1990), 525-543.

[15] P. Walters, Introduction to Ergodic Theory, Springer-Verlag, Berlin, 1982.

Keywords and phrases: large deviations, non-additive sequences, thermodynamic formalism.

 


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