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1 results

  • Smooth orbit equivalence rigidity for dissipative geodesic flows

  • Part of
  • JAVIER ECHEVARRÍA CUESTA
  • Journal:
    Ergodic Theory and Dynamical Systems , First View
    Published online by Cambridge University Press:
    26 May 2025, pp. 1-30
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  • Let M be a smooth closed oriented surface. Gaussian thermostats on M correspond to the geodesic flows arising from metric connections, including those with non-zero torsion. These flows may not preserve any absolutely continuous measure. We prove that if two Gaussian thermostats on M with negative thermostat curvature are related by a smooth orbit equivalence isotopic to the identity, then the two background metrics are conformally equivalent via a smooth diffeomorphism of M isotopic to the identity. We also give a relationship between the thermostat forms themselves. Finally, we prove the same result for Anosov magnetic flows.