A Variational Principle for Topological Pressure for Certain Non-compact Sets
نویسنده
چکیده
Let (X, d) be a compact metric space, f : X 7→ X be a continuous map with the specification property, and φ : X 7→ 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 { x ∈ X : lim n→∞ 1 n n−1 ∑ i=0 φ(f (x)) = α } . 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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