Barkat, Meriem2024-06-242024-06-242024-06-12MD/26http://10.10.1.6:4000/handle/123456789/5041Our thesis isdividedinthreeparts,thefirstpartconsistsinsolvingthesecondpartofthe extended 16thHilbertproblemforaclassofdiscontinuouspiecewisedifferentialsystems.The second partfocusesonfindingthemaximumnumberoflimitcyclesofsmallamplitudewhichis called thecyclictyproblem,andthethirdpartwewereabletofindtheglobalphaseportraitsand the bifurcationsetsforsomespecificfamiliesofdiscontinuouspiecewisequadraticdifferential systems, characterizedbyhavingapseudo-centreattheoriginenPiecewise differentialsystem,Linearcenter,Hamiltonianisochronousglobalcenter,Averaging theory,Pseudo-center,PhaseportraitSyst`emesdiff´erentielsparmorceaux,centrelin´eaire,CentreglobalisochroneHamiltonien, Th´eoriedelamoyenne,Pseudo-centre,Portraitdephase.Phase planes and bifurcations in planar linear-quadratic differential systems with a pseudo-focusThesis