Abstract
In this paper we study non-degenerate centers of planar polynomial Hamiltonian systems. We prove that if the differential system has degree four then the period function of the center tends to infinity as we approach to the boundary of its period annulus. The proof takes advantage of the geometric properties of the period annulus in the Poincare disc and it requires the study of the so called cubic-like Hamiltonian systems, namely the differential systems associated to a Hamiltonian function of the formH(x, y)=A(x)+B(x)y+C(x)y 2+D(x)y 3. Concerning the centers of this family of differential systems, we obtain an analytic expression of its period function. From our point of view this expression constitutes the first step in order to find the isochronicity conditions in the family.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.