Abstract
The tangential center problem was solved by Yu. S. Ilyashenko in the generic case Mat Sbornik (New Series), 78, 120, 3,360–373, (1969). With the aim of having well-understood models of non-generic Hamiltonians, we consider here a family of non-generic Hamiltonians, whose Hamiltonian is of the form \(F=\prod f_{j}\), where fj are real polynomials of degree ≥ 1. For this family, the genericity assumption of transversality at infinity fails and the coincidence of the critical values for different critical points is allowed. We consider some geometric conditions on these polynomials in order to compute the orbit under monodromy of their vanishing cycles. Under those conditions, we provide a solution of the tangential center problem for this family.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
