An Extension of the Bolsinov-Fomenko Theorem on Orbital Classification of Integrable Hamiltonian Systems

Rocky Mountain Journal of Mathematics ◽

10.1216/rmjm/1022009275 ◽

2000 ◽

Vol 30 (2) ◽

pp. 447-476 ◽

Author(s):

A. Cavicchioli ◽

D. Repovš ◽

A.B. Skopenkov

Keyword(s):

Hamiltonian Systems ◽

Integrable Hamiltonian Systems

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A smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom

Sbornik Mathematics ◽

10.1070/sm1995v186n01abeh000001 ◽

1995 ◽

Vol 186 (1) ◽

pp. 1-27 ◽

Author(s):

A V Bolsinov

Keyword(s):

Hamiltonian Systems ◽

Degrees Of Freedom ◽

Integrable Hamiltonian Systems ◽

Two Degrees Of Freedom ◽

Trajectory Classification

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Isoenergetic classification of integrable Hamiltonian systems in a neighborhood of a simple elliptic point

Mathematical Notes ◽

10.1007/bf02110377 ◽

1994 ◽

Vol 55 (5) ◽

pp. 496-501 ◽

Author(s):

L. M. Lerman ◽

Ya. L. Umanskii

Keyword(s):

Hamiltonian Systems ◽

Integrable Hamiltonian Systems ◽

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Smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom. The case of systems with planar atoms

Russian Mathematical Surveys ◽

10.1070/rm1994v049n03abeh002260 ◽

1994 ◽

Vol 49 (3) ◽

pp. 181-182

Author(s):

A V Bolsinov

Keyword(s):

Hamiltonian Systems ◽

Degrees Of Freedom ◽

Integrable Hamiltonian Systems ◽

Two Degrees Of Freedom ◽

Trajectory Classification

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Orbital Classification of Integrable Hamiltonian Systems with Two Degrees of Freedom. The Second Step

Integrable Hamiltonian Systems ◽

10.1201/9780203643426-12 ◽

2004 ◽

pp. 271-314

Keyword(s):

Hamiltonian Systems ◽

Degrees Of Freedom ◽

Second Step ◽

Integrable Hamiltonian Systems ◽

Two Degrees Of Freedom

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Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity

Russian Mathematical Surveys ◽

10.1070/rm1990v045n02abeh002344 ◽

1990 ◽

Vol 45 (2) ◽

pp. 59-94 ◽

Author(s):

A V Bolsinov ◽

S V Matveev ◽

A T Fomenko

Keyword(s):

Hamiltonian Systems ◽

Degrees Of Freedom ◽

Topological Classification ◽

Integrable Hamiltonian Systems ◽

Two Degrees Of Freedom

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Orbital invariants of integrable Hamiltonian systems. The case of simple systems. Orbital classification of systems of Euler type in rigid body dynamics

Izvestiya Mathematics ◽

10.1070/im1995v059n01abeh000003 ◽

1995 ◽

Vol 59 (1) ◽

pp. 63-100 ◽

Author(s):

A V Bolsinov ◽

A T Fomenko

Keyword(s):

Hamiltonian Systems ◽

Rigid Body Dynamics ◽

Integrable Hamiltonian Systems ◽

Body Dynamics ◽

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Orbital Classification of Integrable Hamiltonian Systems with Two Degrees of Freedom. The Second Step

Integrable Hamiltonian Systems ◽

10.1201/9780203643426.ch8 ◽

2004 ◽

Keyword(s):

Hamiltonian Systems ◽

Degrees Of Freedom ◽

Second Step ◽

Integrable Hamiltonian Systems ◽

Two Degrees Of Freedom

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CLASSIFICATION OF FOUR-DIMENSIONAL INTEGRABLE HAMILTONIAN SYSTEMS AND POISSON ACTIONS OF $ \mathbb{R}^2$ IN EXTENDED NEIGHBORHOODS OF SIMPLE SINGULAR POINTS. II

Sbornik Mathematics ◽

10.1070/sm1994v078n02abeh003481 ◽

1994 ◽

Vol 78 (2) ◽

pp. 479-506 ◽

Author(s):

L M Lerman ◽

Ya L Umanskiĭ

Keyword(s):

Hamiltonian Systems ◽

Singular Points ◽

Integrable Hamiltonian Systems ◽

Poisson Actions

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Liouville classification of integrable Hamiltonian systems on surfaces of revolution

Moscow University Mathematics Bulletin ◽

10.3103/s002713221505006x ◽

2015 ◽

Vol 70 (5) ◽

pp. 220-222 ◽

Author(s):

E. O. Kantonistova

Keyword(s):

Hamiltonian Systems ◽

Surfaces Of Revolution ◽

Integrable Hamiltonian Systems

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2. Morse theory of completely integrable Hamiltonian systems. Topology of the level surfaces of constant energy of Hamiltonian systems, obstructions to integrability, classification of rearrangements of general position of Liouville tori in a neighborhood of a bifurcation diagram

Journal of Soviet Mathematics ◽

10.1007/bf01127021 ◽

1987 ◽

Vol 39 (3) ◽

pp. 2688-2693

Keyword(s):

Bifurcation Diagram ◽

Hamiltonian Systems ◽

Morse Theory ◽

General Position ◽

Integrable Hamiltonian Systems ◽

Constant Energy ◽

Completely Integrable ◽

Liouville Tori ◽

Completely Integrable Hamiltonian Systems

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