THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A PERTURBATION OF HYPERELLIPTIC HAMILTONIAN SYSTEM WITH DEGENERATED POLYCYCLE

DOI10.1142/S0218127413500478zbMath1270.34057OpenAlexW1976645861MaRDI QIDQ2845171

Dongmei Xiao, Mao'an Han, Ji Hua Wang

Publication date: 22 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127413500478

zbMATH Keywords

abelian integralweakened Hilbert 16th problemdegenerated polycyclehyperelliptic Hamiltonian

Mathematics Subject Classification ID

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) Asymptotic expansions of solutions to ordinary differential equations (34E05) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Bifurcation of limit cycles from a heteroclinic loop with two cusps ⋮ Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis ⋮ A new approach of asymmetric homoclinic and heteroclinic orbits construction in several typical systems based on the undetermined Padé approximation method ⋮ A new Chebyshev criterion and its application to planar differential systems

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