Topological classification of integrable geodesic flows on orientable two-dimensional Riemannian manifolds with additional integral depending on momenta linearly or quadratically

DOI10.1007/BF01087536zbMath0804.58042OpenAlexW1999348407WikidataQ115394161 ScholiaQ115394161MaRDI QIDQ1326930

Nguyen Tien Zung, L. S. Polyakova, Elena N. Selivanova

Publication date: 13 July 1994

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01087536

zbMATH Keywords

Riemannian metricgeodesic flowcodeLiouville metric

Mathematics Subject Classification ID

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

Liouville foliations of topological billiards with slipping ⋮ Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae ⋮ Singularities of integrable geodesic flows on multidimensional torus and sphere ⋮ Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals ⋮ The Chaplygin case in dynamics of a rigid body in fluid is orbitally equivalent to the Euler case in rigid body dynamics and to the Jacobi problem about geodesics on the ellipsoid ⋮ Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards ⋮ Singular Bohr–Sommerfeld rules for 2D integrable systems

Cites Work

• Unnamed Item
• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• Resonance regions for Mathieu type dynamical systems on a torus
• Bifurcations and stability of families of diffeomorphisms
• Attractors on an N-torus: Quasiperiodicity versus chaos
• Pseudocharacters on the group \(\text{SL}(2,\mathbb{Z})\)
• Scaling of the Arnold tongues
• Resonance Zones in Two-Parameter Families of Circle Homeomorphisms
• Rotation Sets of Toral Flows
• Rotation Sets for Maps of Tori
• Resonance regions for families of torus maps
• Small denominators. I. Mappings of the circumference onto itself