Explosion of differentiability for equivalencies between Anosov flows on 3-manifolds

Bessa, Mário; Dias, Sérgio; Pinto, Alberto

doi:10.1090/proc/12977

Explosion of differentiability for equivalencies between Anosov flows on $3$-manifolds
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by Mário Bessa, Sérgio Dias and Alberto A. Pinto PDF

Proc. Amer. Math. Soc. 144 (2016), 3757-3766 Request permission

Abstract:

For Anosov flows obtained by suspensions of Anosov diffeomorphisms on surfaces, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point, then the conjugacy has a smooth extension to the suspended $3$-manifold. This result generalizes the similar ones of Sullivan and Ferreira-Pinto for 1-dimensional expanding dynamics and also a result of Ferreira-Pinto for 2-dimensional hyperbolic dynamics.

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