Perturbations of quadratic Hamiltonian two-saddle cycles (Q2347864)

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English	Perturbations of quadratic Hamiltonian two-saddle cycles	scientific article

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scholarly article

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Perturbations of quadratic Hamiltonian two-saddle cycles (English)

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zbMATH Open document ID

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10.1016/j.anihpc.2013.12.001

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Lyubomir Gavrilov

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Annales de l'Institut Henri Poincaré. Analyse Non Linéaire

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publication date

10 June 2015

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full work available at URL

https://arxiv.org/abs/1306.2340

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Mathematics Subject Classification ID

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zbMATH DE Number

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MaRDI profile type

MaRDI publication profile

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Cyclicity of unbounded semi-hyperbolic 2-saddle cycles in polynomial Liénard systems

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Alien limit cycles near a Hamiltonian 2-saddle cycle

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Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle

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The cyclicity of period annuli of degenerate quadratic Hamiltonian systems with elliptic segment loops

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Alien limit cycles in Liénard equations

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A survey of quadratic systems

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Hilbert's 16th problem for quadratic vector fields

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Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals

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Abelian integrals and limit cycles

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Successive derivatives of a first return map, application to the study of quadratic vector fields

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The infinitesimal 16th Hilbert problem in the quadratic case

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Cyclicity of period annuli and principalization of Bautin ideals

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On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields

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On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields

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Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems

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The displacement map associated to polynominal unfoldings of planar Hamiltonian vector fields

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On the number of limit cycles arising from perturbations of homoclinic loops of quadratic integrable systems

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On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems

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On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems

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Higher-order Melnikov functions for degenerate cubic Hamiltonians

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Perturbations of quadratic centers

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Centennial History of Hilbert's 16th Problem

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The cyclicity of the elliptic segment loops of the reversible quadratic Hamiltonian systems under quadratic perturbations

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Detecting alien limit cycles near a Hamiltonian 2-saddle cycle

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Non-oscillation of elliptic integrals

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On the number of limit cycles of the equation \frac{𝑑𝑦}𝑑𝑥=\frac{𝑃(𝑥,𝑦)}𝑄(𝑥,𝑦)’ where 𝑃 and 𝑄 are polynomials of the second degree

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Bifurcation of planar vector fields and Hilbert's sixteenth problem

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Melnikov functions and Bautin ideal

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Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment

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On cyclicity of triangles and segments in quadratic systems

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