Spectral estimates for Ruelle operators with two parameters and sharp large deviations

Abstract

We obtain spectral estimates for the iterations of Ruelle operator $L_{f+(a+ıb)\tau +(c+ıd)g}$ with two complex parameters and Hölder functions $f,g$ generalizing the case $\mathrm{Pr}(f)=0$ studied in [PeS2]. As an application we prove a sharp large deviation theorem concerning exponentially shrinking intervals which improves the result in [PeS1].

arXiv admin note: substantial text overlap with arXiv:1409.0721

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