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Smooth conjugacy classes of 3d Axiom A flows

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Abstract

We show a rigidity result for 3-dimensional contact Axiom A flows: given two 3D contact Axiom A flows Φ_1, Φ_2 whose restrictions Φ_1|Λ_1 , Φ_2|Λ_2 to basic sets Λ_1, Λ_2 are orbit equivalent, we prove that if periodic orbits in correspondence have the same length, then the conjugacy is as regular as the flows and respects the contact structure, extending a previous result due to Feldman-Ornstein [23]. Some of the ideas are reminiscent of the work of Otal [54]. As an application, we show that the billiard maps of two open dispersing billiards without eclipse and with the same marked length spectrum are smoothly conjugated.
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Dates and versions

hal-03852329 , version 1 (14-11-2022)

Identifiers

  • HAL Id : hal-03852329 , version 1

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Anna Florio, Martin Leguil. Smooth conjugacy classes of 3d Axiom A flows. 2022. ⟨hal-03852329⟩
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