Perturbations of quadratic hamiltonian systems with symmetry

Emil Ivanov Horozov; Iliya Dimov Iliev

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Displaying similar documents to “Perturbations of quadratic hamiltonian systems with symmetry”

Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields

Markov, Yavor (1996)

Serdica Mathematical Journal

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We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.

Abelian integrals of quadratic Hamiltonian vector fields with an invariant straight line.

Chengzhi Li, Jaume Llibre, Zhi-fen Zhang (1995)

Publicacions Matemàtiques

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We prove that the lowest upper bound for the number of isolated zeros of the Abelian integrals associated to quadratic Hamiltonian vector fields having a center and an invariant straight line after quadratic perturbations is one.

Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.

Yulin Zhao, Zhifen Zhang (2000)

Publicacions Matemàtiques

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It is proved in this paper that the maximum number of limit cycles of system ⎧ dx/dt = y ⎨ ⎩ dy/dt = kx - (k + 1)x² + x³ + ε(α + βx + γx²)y is equal to two in the finite plane, where k > (11 + √33) / 4 , 0 < |ε| << 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.

Existence and distribution of limit cycles in a Hamiltonian system.

Tigan, Gheorghe (2006)

Applied Mathematics E-Notes [electronic only]

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Perturbations of Systems Describing the Motion of a Particle in Central Fields

Christov, Ognyan, Dragnev, Dragomir (1995)

Serdica Mathematical Journal

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The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.

Solutions with minimal period for hamiltonian systems in a potential well

Antonio Ambrosetti, Vittorio Coti Zelati (1987)

Annales de l'I.H.P. Analyse non linéaire

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Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point

Antonio Giorgilli (1988)

Annales de l'I.H.P. Physique théorique

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The null divergence factor.

Javier Chavarriga, Héctor Giacomini, Jaume Giné (1997)

Publicacions Matemàtiques

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Let (P,Q) be a C vector field defined in a open subset U ⊂ R. We call a null divergence factor a C solution V (x, y) of the equation P ∂V/∂x + Q ∂V/ ∂y = ( ∂P/∂x + ∂Q/∂y ) V. In previous works it has been shown that this function plays a fundamental role in the problem of the center and in the determination of the limit cycles. In this paper we show how to construct systems with a given null divergence factor. The method presented in this paper is a generalization of the classical Darboux...