A uniform estimate for rate functions in large deviations

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    Given Hölder continuous functions f and ψ on a subshift of finite type ΣA+ such that ψ is not cohomologous to a constant, the classical large deviation principle holds with a rate function Iψ⩾ 0 such that Iψ(p) = 0 iff [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.] is the equilibrium state of f. In this paper we derive a uniform estimate from below for Iψ for p outside an interval containing [InlineEquation not available: see fulltext.], which depends only on the subshift ΣA+, 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.

    Original languageEnglish
    Pages (from-to)1013-1022
    Number of pages10
    JournalEuropean Journal of Mathematics
    Issue number4
    Publication statusPublished - 1 Dec 2016

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