A subadditive thermodynamic formalism for mixing repellers

Abstract

The thermodynamical description of fractals that has recently attracted much interest both experimentally and theoretically in the study of dynamical systems is, in some ways, limited, being essentially an additive theory. The author presents a subadditive thermodynamic formalism for which he derives a variational principle and shows how it may be used to study the dynamics of non-conformal transformations. In particular the author discusses an analogue of Bowen's formula for the dimension of a mixing repeller.