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- W3136207067 abstract "We prove a radial source estimate in Hölder–Zygmund spaces for uniformly hyperbolic dynamics (also known as Anosov flows), in the spirit of Dyatlov–Zworski [DZ16]. The main consequence is a new linear stability estimate for the marked length spectrum rigidity conjecture, also known as the Burns–Katok [BK85] conjecture. We show in particular that in any dimension ≥2, in the space of negatively-curved metrics, C 3+ε -close metrics with same marked length spectrum are isometric. This improves recent works of Guillarmou–Knieper and the second author [GKL22, GL19]. As a byproduct, this approach also allows to retrieve various regularity statements known in hyperbolic dynamics and usually based on Journé’s lemma: the smooth Livšic Theorem of de La Llave–Marco–Moriyón [LMM86], the smooth Livšic cocycle theorem of Niticā–Török [NT98] for general (finite-dimensional) Lie groups, the rigidity of the regularity of the foliation obtained by Hasselblatt [Has92] and others." @default.
- W3136207067 created "2021-03-29" @default.
- W3136207067 creator A5039240988 @default.
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- W3136207067 date "2023-10-02" @default.
- W3136207067 modified "2023-10-03" @default.
- W3136207067 title "Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics" @default.
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- W3136207067 doi "https://doi.org/10.5802/ahl.175" @default.
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