Unfolding of a Quadratic Integrable System with a Homoclinic Loop

(整期优先)网络出版时间:2002-04-14
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<正>Inthispaper,wemakeacompletestudyoftheunfoldingofaquadraticintegrablesystemwithahomoclinicloop.MakingaPoincaretransformationandusingsomenewtechniquestoestimatethenumberofzerosofAbelianintegrals,weobtainthecompletebifurcationdiagramandallphaseportraitsofsystemscorrespondingtodifferentregionsintheparameterspace.Inparticular,weprovethattwoisthemaximalnumberoflimitcyclesbifurcatingfromthesystemunderquadraticnon-conservativeperturbations.