Imane Benabdallah, Benabdallah2024-06-242024-06-242024-06-12MD/25http://10.10.1.6:4000/handle/123456789/5042Our thesisisdevotedtosolvingasignificantandchallengingissueinthequalitativetheory of differentialsystemscalledthesixteenthHilbertproblem.Moreprecisely,weusethefirst integralstodeterminethemaximumnumberoflimitcyclesofsomefamiliesofdiscontinuous piecewise nonlineardifferentialsystemsseparatedbyastraightlineenPiecewise differentialsystem,linearcenter,cubicreversibleisochronouscentershavingrational first integrals,Hamiltoniansystemwithlinearpluscubichomogeneoustermswithanilpotent saddle, limitcycle.Limit cycles of continuous and discontinuous piecewise differential systems separated by straight line and formed by two arbitrary quadratic centersThesis