# American Institute of Mathematical Sciences

July  2012, 32(7): 2521-2531. doi: 10.3934/dcds.2012.32.2521

## The Ruelle spectrum of generic transfer operators

 1 Université d’Avignon, Laboratoire d’Analyse non linéraire et Géométrie, 33, rue Louis Pasteur, 84000, France

Received  December 2009 Revised  July 2010 Published  March 2012

We define a natural space of transfer operators related to holomorphic contraction systems. We show that the classical upper bounds on the Ruelle eigenvalue sequence are optimal for a dense set of transfer operators. A similar statement is derived for Perron-Frobenius operators related to uniformly expanding piecewise real analytic interval maps. The proof is based on potential theory.
Citation: Frédéric Naud. The Ruelle spectrum of generic transfer operators. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2521-2531. doi: 10.3934/dcds.2012.32.2521
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