Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields
Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields
It is proved in the paper that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one centre at most two limit cycles can appear and this bound is exact. A Hamiltonian field \(H\) is generic if no level set contains a straight line. The paper speaks also about related questions (Hilbert's 16th problem, zeroes of Abelian integrals etc.). The methods of proofs are very geometrical. The author is related to the group of E. Horozov, but the paper is very original even if in the spirit of Horozov's work, as the author acknowledges.
- Institute of Mathematics and Informatics Bulgaria
- Bulgarian Academy of Sciences Bulgaria
Hamiltonians, Limit Cycles, limit cycles, Abelian integrals, Bifurcations of limit cycles and periodic orbits in dynamical systems, saddles, centres, Abelian Integrals, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Picard-Lefschetz Formula
Hamiltonians, Limit Cycles, limit cycles, Abelian integrals, Bifurcations of limit cycles and periodic orbits in dynamical systems, saddles, centres, Abelian Integrals, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Picard-Lefschetz Formula
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