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Journal of the London Mathematical Society Advance Access originally published online on September 4, 2009
Journal of the London Mathematical Society 2009 80(3):585-602; doi:10.1112/jlms/jdp041
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© 2009 London Mathematical Society

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

Daniel Thompson

Department of Mathematics
The Pennsylvania State University
University Park
State College
PA 16802
USA

Let (X, d) be a compact metric space, let f:X ↦ X be a continuous map with the specification property and let {varphi}: 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


Formula

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.

2000 Mathematics Subject Classification 37C45 (primary).

This work was supported by EPSRC.

Received October 9, 2008; revised March 10, 2009; published online September 4, 2009.


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