This thesis investigates the limit cycle bifurcation problem of planar piecewise polynomial systems, whose unperturbed system has a center at the origin an‎d may have invariant multiply lines. By Melnikov function method, this thesis provides the upper an‎d lower bounds for the Poincare cyclicity. In particular, the exact cyclicities of two specific cases are given using analyzing method, one of which has been discussed in the paper. We also study a class of planar piecewise smooth quadratic integrable non-Hamiltonian systems, which have a center. By using the averaging method, we give an estimation of the number of limit cycles which bifurcate from the above periodic annulus under the polynomial perturbation of degree n. Our estimation is linear depending on n an‎d it is at least twice the associated estimation of smooth systems.

رسول عاشقي حسين آبادي

حميدرضا مرزبان , رسول كاظمي