ON TYPICAL TOPOLOGICAL PROPERTIES OF INTEGRABLE HAMILTONIAN SYSTEMS

DOI10.1070/IM1989v032n02ABEH000772zbMath0667.58014OpenAlexW1972775213MaRDI QIDQ3819730

A. T. Fomenko, Heiner Zieschang

Publication date: 1989

Published in: Mathematics of the USSR-Izvestiya (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im1989v032n02abeh000772

zbMATH Keywords

periodic solutionsintegrable systemsHamiltonian systemsfundamental groupsconstant energy surface

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (20)

Liouville foliations of topological billiards with slipping ⋮ The Liouville foliation of nonconvex topological billiards ⋮ Algebra and Geometry Through Hamiltonian Systems ⋮ Integrable topological billiards and equivalent dynamical systems ⋮ Classification of singularities of the Liouville foliation of an integrable elliptical Billiard with a potential of fourth degree ⋮ Integrable billiard systems realize toric foliations on lens spaces and the 3-torus ⋮ Topological atlas of the Kovalevskaya top in a double field ⋮ Billiard Systems as the Models for the Rigid Body Dynamics ⋮ The Fomenko-Zieschang invariants of nonconvex topological billiards ⋮ Local modeling of Liouville foliations by billiards: implementation of edge invariants ⋮ Integrable perturbations of saddle singularities of rank 0 of integrable Hamiltonian systems ⋮ Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards ⋮ Topological types of isoenergy surfaces in the system of the Chaplygin ball with a rotor ⋮ Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards ⋮ Classification of the gluing matrices on the loop molecules of the points of center-center type ⋮ Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems ⋮ Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: Recent results ⋮ Topological billiards, conservation laws and classification of trajectories ⋮ Topology of Liouville foliations of integrable billiards on table-complexes ⋮ Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

This page was built for publication: ON TYPICAL TOPOLOGICAL PROPERTIES OF INTEGRABLE HAMILTONIAN SYSTEMS