2016/10/26 by Luchezar Stoyanov, Stoyanov, Luchezar
Mathematics · #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.1610.08160
Given Hölder continuous functions f and ψ on a sub-shift of finite type ΣA+ such that ψ is not cohomologous to a constant, the classical large deviation principle holds (\citeOP, \citeKif, \citeY) with a rate function Iψ≥ 0 such that Iψ(p) = 0 iff p = ∫ ψ d μ, where μ= μf is the equilibrium state of f. In this paper we derive a uniform estimate from below for Iψ for p outside an interval containing ψ = ∫ ψ dμ, which depends only on the sub-shift, the function f, the norm |ψ|_∞, the Hölder constant of ψ and the integral ψ. Similar results can be derived in the same way e.g. for Axiom A diffeomorphisms on basic sets.