Document Zbl 1274.37012

Jebrane, Ahmed; Mardešić, Pavao; Pelletier, Michèle

A note on a generalization of Françoise’s algorithm for calculating higher order Melnikov functions. (English) Zbl 1274.37012

Bull. Sci. Math. 128, No. 9, 749-760 (2004).

MSC:

37C10	Dynamics induced by flows and semiflows
34C07	Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations

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References:

[1]	Chen, K.-T., Algebras of iterated path integrals and fundamental groups, Trans. Amer. Math. Soc, 156, 359-379 (1971) · Zbl 0217.47705
[2]	Françoise, J. P., Successive derivatives of a first return map, application to the study of quadratic vector fields, Ergodic Theory Dynam. Systems, 16, 87-96 (1996) · Zbl 0852.34008
[3]	Gavrilov, L.; Iliev, I. D., The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields, v1, 21 May 2003
[4]	Iliev, I. D., The cyclicity of the period annulus of the quadratic Hamiltonian triangle, JDE, 128, 309-326 (1996) · Zbl 0853.58084
[5]	Jebrane, A.; Mardešić, P.; Pelletier, M., A generalization of Françoise’s algorithm for calculating higher order Melnikov functions, Bull. Sci. Math, 126, 705-732 (2002) · Zbl 1029.34081
[6]	Yakovenko, S., A geometric proof of the Bautin theorem, AMS Transl. (2), 165, 203-219 (1995) · Zbl 0828.34026
[7]	Zoladek, H., The cyclicity of triangles and segments in quadratic systems, JDE, 122, 137-159 (1995) · Zbl 0840.34031

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