Transcendental Case in Stability Problem of Hamiltonian System with Two Degrees of Freedom in Presence of First Order Resonance

Qualitative Theory of Dynamical Systems ◽

10.1007/s12346-012-0077-x ◽

2012 ◽

Vol 12 (1) ◽

pp. 207-216 ◽

Author(s):

Boris S. Bardin ◽

Andrzej J. Maciejewski

Keyword(s):

Hamiltonian System ◽

Stability Problem ◽

Degrees Of Freedom ◽

Two Degrees Of Freedom ◽

Order Resonance ◽

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On stability of an autonomous Hamiltonian system with two degrees of freedom under first-order resonance

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(77)90083-1 ◽

1977 ◽

Vol 41 (1) ◽

pp. 20-28 ◽

Author(s):

A.G. Sokol'skii

Keyword(s):

Hamiltonian System ◽

Degrees Of Freedom ◽

Two Degrees Of Freedom ◽

Order Resonance ◽

First Order ◽

Autonomous Hamiltonian System

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On the Constructive Algorithm for Stability Investigation of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in First-Order Resonance Case

Mechanics of Solids ◽

10.3103/s0025654418050023 ◽

2018 ◽

Vol 53 (S2) ◽

pp. 15-25

Author(s):

B. S. Bardin ◽

E. A. Chekina

Keyword(s):

Hamiltonian System ◽

Equilibrium Point ◽

Degrees Of Freedom ◽

Resonance Case ◽

Two Degrees Of Freedom ◽

Order Resonance ◽

Stability Investigation ◽

First Order ◽

Constructive Algorithm ◽

Periodic Hamiltonian System

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About a constructive algorithm for studying the stability of the equilibrium state of a periodic Hamiltonian system with two degrees of freedom in the case of a first-order resonance

Прикладная математика и механика ◽

10.31857/s003282350000197-6 ◽

2018 ◽

pp. 414-426

Author(s):

B. Bardin ◽

◽

E. Chekina ◽

◽

Keyword(s):

Hamiltonian System ◽

Equilibrium State ◽

Degrees Of Freedom ◽

Two Degrees Of Freedom ◽

Order Resonance ◽

First Order ◽

Constructive Algorithm ◽

The Stability ◽

Periodic Hamiltonian System

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On the Constructive Algorithm for Stability Analysis of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in the Second-order Resonance Case

Regular and Chaotic Dynamics ◽

10.1134/s1560354717070048 ◽

2017 ◽

Vol 22 (7) ◽

pp. 808-823 ◽

Author(s):

Boris S. Bardin ◽

Evgeniya A. Chekina

Keyword(s):

Stability Analysis ◽

Hamiltonian System ◽

Equilibrium Point ◽

Degrees Of Freedom ◽

Second Order ◽

Resonance Case ◽

Two Degrees Of Freedom ◽

Order Resonance ◽

Constructive Algorithm ◽

Periodic Hamiltonian System

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Large excursions of action within the resonance of a degenerate Hamiltonian system with two degrees of freedom

Physical Review E ◽

10.1103/physreve.80.026216 ◽

2009 ◽

Vol 80 (2) ◽

Author(s):

Jian Li ◽

Wei-Dong Li ◽

Jie Liu ◽

Yi-Sui Sun

Keyword(s):

Hamiltonian System ◽

Degrees Of Freedom ◽

Two Degrees Of Freedom

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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

Sbornik Mathematics ◽

10.1070/sm1996v187n04abeh000122 ◽

1996 ◽

Vol 187 (4) ◽

pp. 495-524 ◽

Author(s):

V S Matveev

Keyword(s):

Hamiltonian System ◽

Topological Structure ◽

Degrees Of Freedom ◽

Integrable Hamiltonian System ◽

Two Degrees Of Freedom ◽

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On the stability of a nonautonomous hamiltonian system with two degrees of freedom

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(69)90071-9 ◽

1969 ◽

Vol 33 (3) ◽

pp. 550-557 ◽

Author(s):

A.P. Markeev

Keyword(s):

Hamiltonian System ◽

Degrees Of Freedom ◽

Two Degrees Of Freedom ◽

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Asymptotic trajectories and the stability of the periodic motions of an autonomous hamiltonian system with two degrees of freedom

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(88)90079-2 ◽

1988 ◽

Vol 52 (3) ◽

pp. 283-289

Author(s):

A.P. Markeyev

Keyword(s):

Hamiltonian System ◽

Degrees Of Freedom ◽

Periodic Motions ◽

Two Degrees Of Freedom ◽

Autonomous Hamiltonian System ◽

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On the non-existence of a supplementary meromorphic first integral in a Hamiltonian system with two degrees of freedom in the case of a bifurcation of solutions of an inhomogeneous reduced variational system

Russian Mathematical Surveys ◽

10.1070/rm1998v053n05abeh000087 ◽

1998 ◽

Vol 53 (5) ◽

pp. 1108-1109

Author(s):

S L Ziglin

Keyword(s):

Hamiltonian System ◽

Degrees Of Freedom ◽

First Integral ◽

Variational System ◽

Two Degrees Of Freedom ◽

Bifurcation Of Solutions

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The Classification of the Bifurcations Emerging in the case of an Integrable Hamiltonian System with Two Degrees of Freedom when an Isoenergetic Surface is Non-Compact

Journal of Nonlinear Mathematical Physics ◽

10.2991/jnmp.2004.11.s1.16 ◽

2004 ◽

Vol 11 (sup1) ◽

pp. 122-129

Author(s):

Galina Goujvina

Keyword(s):

Hamiltonian System ◽

Degrees Of Freedom ◽

Integrable Hamiltonian System ◽

Two Degrees Of Freedom ◽

Isoenergetic Surface

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