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

Vesselin Petkov; Luchezar Stoyanov

doi:10.3934/dcds.2019277

Article Contents

2019, Volume 39, Issue 11: 6391-6417. Doi: 10.3934/dcds.2019277

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

Vesselin Petkov^1, and
Luchezar Stoyanov^2,

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: October 31, 2018

Revised: March 31, 2019

Published: August 2019

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Abstract

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].

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Mathematics Subject Classification: Primary: 37C30; Secondary: 37D20, 37C35.

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References

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