Mathematical Research Letters

Volume 25 (2018)

Number 5

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

Pages: 1405 – 1427



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)


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.

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