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Lower bounds for the Ruelle spectrum of analytic expanding circle maps

Published online by Cambridge University Press:  04 May 2017

OSCAR F. BANDTLOW  and
FRÉDÉRIC NAUD
OSCAR F. BANDTLOW
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK email [email protected]
FRÉDÉRIC NAUD
Affiliation:
Laboratoire de Mathématiques d’Avignon, Université d’Avignon, Campus Jean-Henri Fabre, 301 rue de Baruch de Spinoza, 84916 Avignon cedex 9, France email [email protected]
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Abstract

We prove that there exists a dense set of analytic expanding maps of the circle for which the Ruelle eigenvalues enjoy exponential lower bounds. The proof combines potential theoretic techniques and explicit calculations for the spectrum of expanding Blaschke products.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 2 , February 2019 , pp. 289 - 310
Copyright
© Cambridge University Press, 2017 

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