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

Thompson, Daniel
December 2009
Journal of the London Mathematical Society;Dec2009, Vol. 80 Issue 3, p585
Academic Journal
Let (X, d) be a compact metric space, let f:X ↦ X be a continuous map with the specification property and let ϕ: X ↦ ℝ 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.


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