Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems

DOI10.1007/978-3-319-96755-4_2zbMath1419.37055OpenAlexW2902728011MaRDI QIDQ5223385

A. T. Fomenko, Kirill I. Solodskih

Publication date: 18 July 2019

Published in: Understanding Complex Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-96755-4_2

zbMATH Keywords

Reidemeister torsionHamiltonian systemFomenko-Zieschang invariantLiouville foliationisoenergy manifold

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Liouville classification of integrable Hamiltonian systems on surfaces of revolution
• Integrable billiards model important integrable cases of rigid body dynamics
• Topological invariants of Liouville integrable Hamiltonian systems
• Topological classification of integrable geodesic flows in a potential field on the torus of revolution
• Topological invariants for elliptical billiards and geodesics on ellipsoids in the Minkowski space
• Topological Classification of Geodesic Flows on Revolution 2-Surfaces with Potential
• Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution
• Classification of billiard motions in domains bounded by confocal parabolas
• Algebra and Geometry Through Hamiltonian Systems
• Billiard Systems as the Models for the Rigid Body Dynamics
• Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation
• A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM
• Maximally symmetric cell decompositions of surfaces and their coverings
• The topology of Liouville foliation for the Sokolov integrable case on the Lie algebra so(4)
• Reidemeister torsion in knot theory
• THE TOPOLOGY OF SURFACES OF CONSTANT ENERGY IN INTEGRABLE HAMILTONIAN SYSTEMS, AND OBSTRUCTIONS TO INTEGRABILITY
• ON TYPICAL TOPOLOGICAL PROPERTIES OF INTEGRABLE HAMILTONIAN SYSTEMS
• THE TOPOLOGY OF INTEGRAL SUBMANIFOLDS OF COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS
• Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry
• Computation of the fine Fomenko-Zieschang invariant for the main integrable cases of rigid body motion
• Graph-manifolds and integrable Hamiltonian systems

This page was built for publication: Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems