Mathematical Research Letters

Volume 25 (2018)

Number 5

Horocyclic invariance of Ruelle resonant states for contact Anosov flows in dimension $3$

Pages: 1405 – 1427

DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n5.a3

Authors

Colin Guillarmou (Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France)

Frédéric Faure (Institut Fourier, Université Grenoble Alpes, CNRS, Saint Martin d’Hères, France)

Abstract

We show that for contact Anosov flows in dimension $3$ the resonant states associated to the first band of Ruelle resonances are distributions that are invariant by the unstable horocyclic flow.

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C.G. is supported by ERC consolidator grant IPFLOW no 725967.

F.F. and C.G. were supported by the grant ANR 13-BS01-0007-01.

Received 20 September 2017

Accepted 15 March 2018

Published 1 February 2019