Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds

DOI10.1070/SM9349zbMath1456.37062OpenAlexW3025768640MaRDI QIDQ5135758

S. S. Nikolaenko

Publication date: 23 November 2020

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm9349

zbMATH Keywords

Hamiltonian systemtopological classification\(f\)-graphtrajectory equivalencenoncompact atom

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Bifurcations of singular points in dynamical systems (37G10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Singularities of vector fields, topological aspects (58K45) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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Modeling the degenerate singularities of integrable billiard systems by billiard books ⋮ Discrete representations of orbit structures of flows for topological data analysis ⋮ First Appelrot class of pseudo-Euclidean Kovalevskaya system ⋮ Billiards with changing geometry and their connection with the implementation of the Zhukovsky and Kovalevskaya cases ⋮ Noncompactness property of fibers and singularities of non-Euclidean Kovalevskaya system on pencil of Lie algebras ⋮ Topology of Liouville foliations of integrable billiards on table-complexes

Cites Work

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• Bifurcation diagrams of natural Hamiltonian systems on Bertrand manifolds
• Topological invariants of Liouville integrable Hamiltonian systems
• Topological equivalence of smooth functions with isolated critical points on a closed surface
• Topological classification of the Goryachev integrable systems in the rigid body dynamics: non-compact case
• An analogue of the Liouville theorem for integrable Hamiltonian systems with incomplete flows
• Classification of billiard motions in domains bounded by confocal parabolas
• The topology of Lagrangian foliations of integrable systems with hyperelliptic Hamiltonian
• Topological features of the Sokolov integrable case on the Lie algebra $ \mathrm{e}(3)$
• A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM
• Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity
• THE TOPOLOGY OF SURFACES OF CONSTANT ENERGY IN INTEGRABLE HAMILTONIAN SYSTEMS, AND OBSTRUCTIONS TO INTEGRABILITY
• The Liouville Arnold Nekhoroshev theorem for non-compact invariant manifolds
• Integrable topological billiards and equivalent dynamical systems
• A smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom
• Orbital invariants of integrable Hamiltonian systems. The case of simple systems. Orbital classification of systems of Euler type in rigid body dynamics
• A smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom
• The topology of integrable systems with incomplete fields

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