Geodesic stretch, pressure metric and marked length spectrum rigidity

We refine the recent local rigidity result for the marked length spectrum obtained by the first and third author in [GL19] and give an alternative proof using the geodesic stretch between two Anosov flows and some uniform estimate on the variance appearing in the central limit theorem for Anosov geo...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 42; no. 3; pp. 974 - 1022
Main Authors GUILLARMOU, COLIN, KNIEPER, GERHARD, LEFEUVRE, THIBAULT
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.03.2022
Subjects
Billiards
Original Article
Rigidity
37D35
Anosov geodesic flows
marked length spectrum
37D40
37C27
rigidity
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Summary:We refine the recent local rigidity result for the marked length spectrum obtained by the first and third author in [GL19] and give an alternative proof using the geodesic stretch between two Anosov flows and some uniform estimate on the variance appearing in the central limit theorem for Anosov geodesic flows. In turn, we also introduce a new pressure metric on the space of isometry classes, which reduces to the Weil–Petersson metric in the case of Teichmüller space and is related to the works [BCLS15, MM08].
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.75