Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties

DOI10.1007/BF01215756zbMath0585.58022MaRDI QIDQ1070613

Henri Epstein, Pierre Collet, Giovanni Gallavotti

Publication date: 1984

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian perturbations of the geodesic flow

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Geodesics in global differential geometry (53C22) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (25)

Invariants for smooth conjugacy of hyperbolic dynamical systems. I ⋮ Invariant distributions for homogeneous flows and affine transformations ⋮ Locating resonances for axiom A dynamical systems ⋮ Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices ⋮ Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives ⋮ Invariants for smooth conjugacy of hyperbolic dynamical systems. II ⋮ Invariants for smooth conjugacy of hyperbolic dynamical systems. III ⋮ The rate of mixing for geodesic and horocycle flows ⋮ Robust exponential decay of correlations for singular-flows ⋮ Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers ⋮ Exponential mixing for smooth hyperbolic suspension flows ⋮ Analyticity of the Sinai-Ruelle-Bowen measure for a class of simple Anosov flows ⋮ Maximally chaotic dynamical systems ⋮ Invariant distributions and time averages for horocycle flows ⋮ Artin billiard: exponential decay of correlation functions ⋮ Exponential mixing for the geodesic flow on hyperbolic three-manifolds ⋮ Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems ⋮ Resonances in chaotic dynamics ⋮ Unnamed Item ⋮ THE g-AREAS AND THE COMMUTATOR LENGTH ⋮ A criterion of integrability for perturbed nonresonant harmonic oscillators. Wick Ordering of the perturbations in classical mechanics and invariance of the frequency spectrum ⋮ Sobolev regularity of solutions of the cohomological equation ⋮ Sampling and Statistical Physics via Symmetry ⋮ On the rate of mixing of Axiom A flows ⋮ Canonical perturbation theory of Anosov systems, and regularity results for the Livsic cohomology equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some inverse spectral results for negatively curved 2-manifolds
• The spectral class of the quantum-mechanical harmonic oscillator
• Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

This page was built for publication: Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties