On the topology of manifolds with completely integrable geodesic flows

DOI10.1017/S0143385700006623zbMath0735.58028OpenAlexW2057021206MaRDI QIDQ3363273

Gabriel P. Paternain

Publication date: 1992

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

Full work available at URL: https://doi.org/10.1017/s0143385700006623

zbMATH Keywords

geodesic flowcompletely integrablesimply connected Riemannian manifoldrationally ellipticmultiplicity free compact action

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Global Riemannian geometry, including pinching (53C20) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (13)

On the topology of manifolds with completely integrable geodesic flows. II ⋮ \(C^0\)-robustness of topological entropy for geodesic flows ⋮ Integrable geodesic flows of nonholonomic metrics ⋮ Collection of problems proposed at International Conference on Variational Methods ⋮ Topological entropy for geodesic flows on fibre bundles over rationally hyperbolic manifolds ⋮ Singularities of integrable and near-integrable Hamiltonian systems ⋮ Invariant fibrations of geodesic flows ⋮ Integrable geodesic flows on surfaces ⋮ Integrable geodesic flows on \(n\)-step nilmanifolds ⋮ Differentiable structures with zero entropy on simply connected 4-manifolds ⋮ Manifolds of infinite topological type with integrable geodesic flows ⋮ Vanishing of the entropy pseudonorm for certain integrable systems ⋮ Loop space homology -- problems and questions

Cites Work

• Sur les variétés à courbure strictement positive
• Topological entropy for geodesic flows
• On the entropy of the geodesic flow in manifolds without conjugate points
• New examples of manifolds with strictly positive curvature
• Convexity properties of the moment mapping
• An exotic sphere with nonnegative sectional curvature
• Contributions of rational homotopy theory to global problems in geometry
• Compact homogeneous Riemannian manifolds with strictly positive curvature
• Integrability and non-integrability in Hamiltonian mechanics
• Entropy for Group Endomorphisms and Homogeneous Spaces
• ON THE RELATIONS AMONG VARIOUS ENTROPY CHARACTERISTICS OF DYNAMICAL SYSTEMS

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