# American Institute of Mathematical Sciences

November  2019, 39(11): 6391-6417. doi: 10.3934/dcds.2019277

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

 1 Université de Bordeaux, Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France 2 University of Western Australia, Department of Mathematics and Statistics, 35 Stirling Highway, Perth WA 6009, Australia

Received  November 2018 Revised  April 2019 Published  August 2019

We obtain spectral estimates for the iterations of Ruelle operators $L_{f + (a + {\bf i} b)\tau + (c + {\bf i} d) g}$ with two complex parameters and Hölder continuous functions $f,\: g$ generalizing the case ${\rm{Pr}}(f) = 0$ studied in [9]. As an application we prove a sharp large deviation theorem concerning exponentially shrinking intervals which improves the result in [8].

Citation: Vesselin Petkov, Luchezar Stoyanov. Spectral estimates for Ruelle operators with two parameters and sharp large deviations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6391-6417. doi: 10.3934/dcds.2019277
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