The thermodynamic formalism for almost-additive sequences

Pages: 435 - 454, Volume 16, Issue 2, October 2006

doi:10.3934/dcds.2006.16.435       Abstract        Full Text (258.6K)       Related Articles

Anna Mummert - Penn State University, McAllister Building, State College, PA 16802, United States (email)

Abstract: We study the nonadditive thermodynamic formalism for the class of almost-additive sequences of potentials. We define the topological pressure $P_Z(\Phi)$ of an almost-additive sequence $\Phi$, on a set $Z$. We give conditions which allow us to establish a variational principle for the topological pressure. We state conditions for the existence and uniqueness of equilibrium measures, and for subshifts of finite type the existence and uniqueness of Gibbs measures. Finally, we compare the results for almost-additive sequences to the thermodynamic formalism for the classical (additive) case [10] [11] [3], the sequences studied by Barreira [1], Falconer [5], and that of Feng and Lau [7], [6].

Keywords:  Thermodynamic formalism, Nonadditive sequences, Equilibrium mea-sures, Gibbs measures.
Mathematics Subject Classification:  Primary: 37C40; Secondary: 82B26.

Received: July 2005;      Revised: December 2005;      Published: July 2006.