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

Markov, Yavor

Displaying similar documents to “Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields”

Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves

Mihajlova, Ana (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08. We obtain an upper bound for the number of zeros of the Abelian integral. The work was partially supported by contract No 15/09.05.2002 with the Shoumen University “K. Preslavski”, Shoumen, Bulgaria.

Perturbations of quadratic hamiltonian systems with symmetry

Emil Ivanov Horozov, Iliya Dimov Iliev (1996)

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

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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.

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.

Existence and distribution of limit cycles in a Hamiltonian system.

Tigan, Gheorghe (2006)

Applied Mathematics E-Notes [electronic only]

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Abelian integrals related to Morse polynomials and perturbations of plane hamiltonian vector fields

Lubomir Gavrilov (1999)

Annales de l'institut Fourier

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Let $𝒜$ be the real vector space of Abelian integrals $I (h) = \int \int_{{H \leq h}} R (x, y) d x \land d y, h \in [0, \tilde{h}]$ where $H (x, y) = (x^{2} + y^{2}) / 2 + ...$ is a fixed real polynomial, $R (x, y)$ is an arbitrary real polynomial and ${H \leq h}$ , $h \in [0, \tilde{h}]$ , is the interior of the oval of $H$ which surrounds the origin and tends to it as $h \to 0$ . We prove that if $H (x, y)$ is a semiweighted homogeneous polynomial with only Morse critical points, then $𝒜$ is a free finitely generated module over the ring of real polynomials $ℝ [h]$ , and compute its rank. We find the generators of $𝒜$ in the case when $H$ is an...

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.