Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2

zbMath1424.34115arXiv1609.09195MaRDI QIDQ4624609

Huanhuan Tian

Publication date: 22 February 2019

Full work available at URL: https://arxiv.org/abs/1609.09195

zbMATH Keywords

limit cyclehomoclinic loopnilpotent saddle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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