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On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems
Author(s) -
Horozov E.,
Iliev I. D.
Publication year - 1994
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-69.1.198
Subject(s) - mathematics , quadratic equation , saddle , hamiltonian (control theory) , limit (mathematics) , hamiltonian system , mathematical analysis , saddle point , limit cycle , pure mathematics , mathematical physics , geometry , mathematical optimization
We prove that in quadratic perturbations of generic quadratic Hamiltonian vector fields with three saddle points and one centre there can appear at most two limit cycles. This bound is exact.