Smooth orbit equivalence rigidity for dissipative geodesic flows

2024/06/02 by Cuesta, Javier Echevarría
#37D40 (Primary) 37C15 #53C24 (Secondary) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.00607

Abstract

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.

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