Integrable geodesic flows with wild first integrals: the case of two-step nilmanifolds

DOI10.1017/S0143385702001517zbMath1063.37049OpenAlexW2023052998MaRDI QIDQ4467699

Leo T. Butler

Publication date: 10 June 2004

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

Full work available at URL: https://doi.org/10.1017/s0143385702001517

zbMATH Keywords

Hamiltonian systemsintegrable geodesic flowstwo-step nilmanifoldsnon abelian Lie groupswild first integrals

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Topological entropy (37B40) Geodesic flows in symplectic geometry and contact geometry (53D25)

Related Items (12)

Topology and Bifurcations in Nonholonomic Mechanics ⋮ On first integrals of the geodesic flow on Heisenberg nilmanifolds ⋮ Topological entropy of left-invariant magnetic flows on 2-step nilmanifolds ⋮ Integrability of geodesic flows and isospectrality of Riemannian manifolds ⋮ On the complete integrability of the geodesic flow of pseudo-\(H\)-type Lie groups ⋮ Invariant fibrations of geodesic flows ⋮ Integrability of invariant geodesic flows on \(n\)-symmetric spaces ⋮ Zero entropy, non-integrable geodesic flows and a non-commutative rotation vector ⋮ Symmetric Killing tensors on nilmanifolds ⋮ The geodesic flow on nilpotent Lie groups of steps two and three ⋮ The geodesic flow on nilmanifolds associated to graphs ⋮ Manifolds of infinite topological type with integrable geodesic flows

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