چكيده انگليسي :
Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields Ghadeer Mohammad g mohammad@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamidreza Zohouri Zangeneh hamidz@cc iut ac ir 2016 MSC 34C07 34C08 Keywords Hamiltonian linear type center Cubic polynomial Vector fields Phase por trait AbstractThis thesis based on the following paper 8 In the qualitative theory of real planar polyno mial differential systems two of the main prob lems are the determination of limit cycles andthe center focus problem i e to distinguish when a singular point is either a focus or a center The notion of center goes back to Poincar He defined a center for a vector field on the realplane as a singular point having a neighborhood filled of periodic orbits with the exception ofthe singular point The classification of the centers of quadratic differential systems startedwith the works of Dulac Kapteyn and Bautin The bifurcation diagrams of all quadraticdifferential systems possessing a center were done by Schlomiuk and Zo adek 1994 Thereare many partial results for the centers of polynomial differential systems of degree largerthan 2 We must mention that Malkin and Vulpe and Sibirsky 1988 1989 characterizedthe centers of the polynomial differential systems with linear and homogeneous nonlinearitieswhich have a pair of eigenvalues of the form i with 0 while we characterize for the
