Rigidity properties of Anosov optical hypersurfaces

DOI10.1017/S0143385707000612zbMath1144.53097arXivmath/0508316OpenAlexW2052652065MaRDI QIDQ3509952

Gabriel P. Paternain, Nurlan S. Dairbekov

Publication date: 25 June 2008

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508316

zbMATH Keywords

Anosov flow

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items

The X-ray transform on a general family of curves on Finsler surfaces ⋮ Pestov's identity on frame bundles and applications ⋮ The boundary rigidity problem in the presence of a magnetic field ⋮ The magnetic ray transform on Anosov surfaces ⋮ Invariant distributions, Beurling transforms and tensor tomography in higher dimensions ⋮ Entropy production in thermostats. II

Cites Work

• Unnamed Item
• Longgitudinal KAM-cocycles and action spectra of magnetic flows
• Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
• Integral geometry of tensor fields on a manifold of negative curvature
• Some inverse spectral results for negatively curved 2-manifolds
• Circular symmetry and the trace formula
• Spectral rigidity of a compact negatively curved manifold
• On Anosov energy levels of convex Hamiltonian systems
• The inverse problem of determining a source in the stationary transport equation for a Hamiltonian system
• On the regularity of the Anosov splitting for twisted geodesic flows
• Invariant two-forms for geodesic flows
• Integral geometry for tensor fields. Transl. from the Russian
• First steps in symplectic topology
• First derivative of topological entropy for Anosov geodesic flows in the presence of magnetic fields
• Some problems of integral geometry on Anosov manifolds
• The asymptotic Maslov index and its applications
• On Anosov energy levels of hamiltonians on twisted cotangent bundles
• SOME SMOOTH ERGODIC SYSTEMS
• Sub-actions for Anosov flows