Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat
Abstract
We study the conjecture of Jarque and Villadelprat stating that every center of a planar polynomial Hamiltonian system of even degree is nonisochronous. This conjecture is proved for quadratic and quartic systems. Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2016
- DOI:
- 10.48550/arXiv.1605.07775
- arXiv:
- arXiv:1605.07775
- Bibcode:
- 2016arXiv160507775C
- Keywords:
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- Mathematics - Dynamical Systems
- E-Print:
- 32 pages