2025/11/27 by Sergi Burniol Clotet, Clotet, Sergi Burniol
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2511.22738
openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
We establish a rigidity result for the unstable foliations of transitive Anosov flows on 3-manifolds: if the unstable foliations of two such flows are equivalent (that is, if there exists a homeomorphism mapping one foliation to the other), then the flows are topologically conjugate up to a constant change of time. This result partially generalizes earlier rigidity theorems for horocyclic flows on compact surfaces of negative curvature, originating in the work of Ratner. In that setting, it is known that equivalence of unstable foliations implies that the underlying surfaces are homothetic.