Abstract. We establish a conditional variational principle for the dimension spectra of almost additive sequences, considering simultaneously Birkhoff averages into the future and into the past. Our approach is based on the existence and uniqueness of equilibrium and Gibbs measures for the class of almost additive sequences, in the context of the nonadditive thermodynamic formalism. This formalism is a generalization of the classical thermodynamic formalism, in which the topological pressure of a single function is replaced by the topological pressure of a sequence of functions.

Mathematics Subject Classification: 37C45, 37D20, 37D35

Print publication: Issue 11 (November 2009)
Received 7 August 2008, in final form 24 September 2009
Published 13 October 2009