Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop

DOI10.1016/j.jde.2020.06.037zbMath1452.34043OpenAlexW3038725750MaRDI QIDQ2202248

Pei Yu, Xian Bo Sun

Publication date: 18 September 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.06.037

zbMATH Keywords

Hopf cyclicityabelian integralhyper-elliptic Hamiltonian systemannulus cyclicity

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (5)

Sharp bound of the number of zeros for a Liénard system with a heteroclinic loop ⋮ Upper Bound on the Number of Zeros of Abelian Integrals for Hyperbolic Hamiltonian Systems of Degree Seven ⋮ Limit cycles near a homoclinic loop connecting a tangent saddle in a perturbed quadratic Hamiltonian system ⋮ Nine limit cycles in a 5-degree polynomials Liénard system ⋮ Existence of solitary waves in a perturbed KdV-mKdV equation

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