The marked length spectrum of Anosov manifolds

DOI10.4007/annals.2019.190.1.6zbMath1506.53054arXiv1806.04218OpenAlexW2964294577WikidataQ127551341 ScholiaQ127551341MaRDI QIDQ2320613

Thibault Lefeuvre, Colin Guillarmou

Publication date: 23 August 2019

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.04218

zbMATH Keywords

rigidityclosed geodesicsmarked length spectrumAnosov geodesic flow

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Rigidity results (53C24) Periodic orbits of vector fields and flows (37C27) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (23)

Isospectral finiteness on convex cocompact hyperbolic 3-manifolds ⋮ Robin spectral rigidity of the ellipse ⋮ Local rigidity of manifolds with hyperbolic cusps. I: Linear theory and microlocal tools ⋮ Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics ⋮ Centrally symmetric analytic plane domains are spectrally determined in this class ⋮ Length spectrum rigidity for piecewise analytic Bunimovich billiards ⋮ Homoclinic orbits, multiplier spectrum and rigidity theorems in complex dynamics ⋮ Marked length spectral determination of analytic chaotic billiards with axial symmetries ⋮ Resonances and weighted zeta functions for obstacle scattering via smooth models ⋮ Circumcenter extension maps for non-positively curved spaces ⋮ Approximate rigidity of the marked length spectrum ⋮ Local rigidity of manifolds with hyperbolic cusps. II: Nonlinear theory ⋮ The covariance metric in the Blaschke locus ⋮ Rigidity of geometric structures ⋮ Marked boundary rigidity for surfaces of Anosov type ⋮ Travelling times in scattering by obstacles in curved space ⋮ The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed ⋮ Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards ⋮ Lyapunov exponents and rigidity of Anosov automorphisms and skew products ⋮ Local marked boundary rigidity under hyperbolic trapping assumptions ⋮ Open problems and questions about geodesics ⋮ Geodesic stretch, pressure metric and marked length spectrum rigidity ⋮ Inverse problems and rigidity questions in billiard dynamics

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