Large deviations for systems with non-uniform structure

Abstract

We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems, including $\beta$-shifts, $S$-gap shifts, and their factors. A crucial step in our approach is to prove a `horseshoe theorem' for these systems.

32 pages. Exposition substantially revised from v1, and some minor mathematical changes. In particular, one of the hypothesis of our main theorem is simpler than in v1. To appear in Transactions of the American Mathematical Society

References in corpus (1)

• Unique equilibrium states for flows and homeomorphisms with non-uniform structure

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