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1 results

  • First Ruelle resonance for an Anosov flow with smooth potential

  • Part of
  • TRISTAN HUMBERT
  • Journal:
    Ergodic Theory and Dynamical Systems , First View
    Published online by Cambridge University Press:
    06 January 2025, pp. 1-37
    • Article
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  • We combine methods from microlocal analysis and dimension theory to study resonances with largest real part for an Anosov flow with smooth real valued potential. We show that the resonant states are closely related to special systems of measures supported on the stable manifolds introduced by Climenhaga [SRB and equilibrium measures via dimension theory. A Vision for Dynamics in the 21st Century: The Legacy of Anatole Katok. Cambridge University Press, Cambridge, 2024, pp. 94–138]. As a result, we relate the presence of the resonances on the critical axis to mixing properties of the flow with respect to certain equilibrium measures and show that these equilibrium measures can be reconstructed from the spectral theory of the Anosov flow.