Melnikov functions - Open Access .click

Journal of Mathematical Analysis and Applications, 2018
Consider a \(C^{\infty}\) smooth family of real planar vector fields \(\left(X_\varepsilon\right)_\varepsilon\) of the form \[ X_\varepsilon (x) \, = \, X_0(x) + \varepsilon X_1(x) + \varepsilon^2 X_2(x) + \, \ldots \, + \varepsilon^n X_n(x) + \mathcal{O}\left(\varepsilon^{n+1}\right), \] for some integer \(n \geq 1\), \(x \in \mathbb{R}^2\) and ...
Adriana Buică
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MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANAR HAMILTONIAN SYSTEM

Chinese Annals of Mathematics Series B, 1999
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Jiang, Qibao, Han, Mao'an
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A note on higher order Melnikov functions

Qualitative Theory of Dynamical Systems, 2005
The paper comments some facts related to the weakened 16th Hilbert's problem about limit cycles. The authors deal with small polynomial perturbations of Hamiltonian systems in the plane \(dH-\varepsilon \omega=0\) such that the first displacement map near a periodic orbit of the unperturbed system is of the form \(\Delta H=\varepsilon^kM_k(h)+O ...
Jebrane, Ahmed, Żołądek, Henryk
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melnikov function
limit cycle
limit cycles

bifurcation
melnikov method
fos: mathematics

mathematics
abelian integrals
dynamical systems math.ds