Coefficient estimates in subclasses of the Carathéodory class related to conical domains.
A class of degree four differential systems that have an invariant conic , , is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.
2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80The Dunkl operators.* Supported by the Tunisian Research Foundation under 04/UR/15-02.
We study isochronous centers of some classes of plane differential systems. We consider systems with constant angular speed, both with homogeneous and nonhomogenous nonlinearities. We show how to construct linearizations and first integrals of such systems, if a commutator is known. Commutators are found for some classes of systems. The results obtained are used to prove the isochronicity of some classes of centers, and to find first integrals for a class of Liénard equations with isochronous centers....