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.

arXiv comment32 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 (7)

• Intrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors
• Unique equilibrium states for flows and homeomorphisms with non-uniform structure
• Equilibrium states beyond specification and the Bowen property
• Large deviations for non-uniformly expanding maps
• Large deviation principles for non-uniformly hyperbolic rational maps
• Intrinsic ergodicity via obstruction entropies
• Large deviation principle for Benedicks-Carleson quadratic maps

Cited by in corpus (13)

• Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets
• Weak Gibbs measures and large deviations
• Large deviation principles of one-dimensional maps for Hölder continuous potentials
• High pointwise emergence and Katok's conjecture for systems with non-uniform structure
• Unique equilibrium states for Bonatti-Viana diffeomorphisms
• Typical periodic optimization for dynamical systems: symbolic dynamics
• On involution kernels and large deviations principles on $\beta$-shifts
• Large deviation principle for linear mod 1 transformations
• Distributional chaos in multifractal analysis, recurrence and transitivity
• Ergodic optimization for continuous functions on non-Markov shifts
• Equilibrium measures of the natural extension of beta-shifts
• A new condition for the genericity of ergodic measures on Riemannian manifolds
• Intrinsic ergodicity for factors of $(-\beta )$-shifts