High order Melnikov functions and the problem of uniformity in global bifurcation

DOI10.1007/BF01759638zbMath0768.34023OpenAlexW2003186893MaRDI QIDQ1199804

Zhi-Fen Zhang, Baoyi Li

Publication date: 16 January 1993

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01759638

zbMATH Keywords

periodic orbitsMelnikov functionhomoclinic loopuniqueness of limit cyclesnumber of limit cyclesautonomously perturbed planar Hamiltonian systemssaddle-loop bifurcation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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