A variational principle for topological pressure for certain non-compact sets

Abstract

Let (X, d) be a compact metric space, let f:X X be a continuous map with the specification property and let φ: X be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form Analogous results were previously known for topological entropy. As an application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification and the dimension spectrum of certain non-uniformly expanding interval maps. © 2009 London Mathematical Society.