Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms (Q5013919)

scientific article; zbMATH DE number 7438611

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English	Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms	scientific article; zbMATH DE number 7438611

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instance of

scholarly article

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title

Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms (English)

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zbMATH Open document ID

1484.37064

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DOI

10.1007/978-3-030-50302-4_1

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Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

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publication date

3 December 2021

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Mathematics Subject Classification ID

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Liouville foliations

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integrable Hamiltonian systems

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billiard conjecture

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-030-50302-4_1

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A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics

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The geodesic flow on a two-dimensional ellipsoid in the field of an elastic force. Topological classification of solutions

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Q3210213

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Some integrable extensions of Jacobi's problem of geodesics on an ellipsoid

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Liouville integrable generalized billiard flows and Poncelet type theorems

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Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards

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Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II

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The Liouville foliation of the billiard book modelling the Goryachev-Chaplygin case

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Topological obstacles to the realizability of integrable Hamiltonian systems by billiards

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Bifurcation sets in an integrable problem on motion of a rigid body in fluid.

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Topological atlas of the Kowalevski-Sokolov top

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Bifurcations of first integrals in the Sokolov case

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Q4011331

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The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)

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Q5186433

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Bifurcation of common levels of first integrals of the Kovalevskaya problem

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Singularities of integrable Hamiltonian systems with the same boundary foliation. An infinite series

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Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(3, 1)\)

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Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra so(4)

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Topological analysis of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(4)\)

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Topological classification of systems of Kovalevskaya-Yehia type

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Classification of nondegenerate equilibria and degenerate 1-dimensional orbits of the Kovalevskaya-Yehia integrable system

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Calculation of the Fomenko-Zieschang invariants in the Kovalevskaya-Yehia integrable case

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Q4463736

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Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations

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The method of loop molecules and the topology of the Kovalevskaya top

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Q4880507

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Maximally symmetric cell decompositions of surfaces and their coverings

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A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM

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ON TYPICAL TOPOLOGICAL PROPERTIES OF INTEGRABLE HAMILTONIAN SYSTEMS

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THE TOPOLOGY OF SURFACES OF CONSTANT ENERGY IN INTEGRABLE HAMILTONIAN SYSTEMS, AND OBSTRUCTIONS TO INTEGRABILITY

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Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case

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An elliptic billiard in a potential force field: classification of motions, topological analysis

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Integrable topological billiards and equivalent dynamical systems

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Integrable billiards model important integrable cases of rigid body dynamics

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Isoenergetic manifolds of integrable billiard books

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Billiards and integrability in geometry and physics. New scope and new potential

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Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems

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Saddle singularities of complexity 1 of integrable Hamiltonian systems

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Integrable perturbations of saddle singularities of rank 0 of integrable Hamiltonian systems

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Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems

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Q3542343

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Integrable Hamiltonian system with two degrees of freedom. The topological structure of saturated neighbourhoods of points of focus-focus and saddle-saddle type

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The symplectic topology of completely integrable Hamiltonian systems

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On global action-angle coordinates

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Q4821521

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Q4939713

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Mathematics(1 entry)

mardi Publication:5013919