The Ruelle spectrum of generic transfer operators

Frédéric Naud

doi:10.3934/dcds.2012.32.2521

Article Contents

2012, Volume 32, Issue 7: 2521-2531. Doi: 10.3934/dcds.2012.32.2521

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The Ruelle spectrum of generic transfer operators

Frédéric Naud^1,

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

Received: November 30, 2009

Revised: June 30, 2010

Published: June 2012

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Abstract

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.

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Mathematics Subject Classification: 37C30, 37D20.

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References

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