On a computer-aided approach to the computation of Abelian integrals

Details On a computer-aided approach to the computation of Abelian integrals On a computer-aided approach to the computation of Abelian integrals

2008-09-17

arxiv.org/abs/0809.2867v3

BIT - Numerical Mathematics 51(3):653-667 (2011)

Mathematics

Dynamical Systems

Scientific paper

10.1007/s10543-011-0318-4

An accurate method to compute enclosures of Abelian integrals is developed.
This allows for an accurate description of the phase portraits of planar
polynomial systems that are perturbations of Hamiltonian systems. As an
example, it is applied to the study of bifurcations of limit cycles arising
from a cubic perturbation of an elliptic Hamiltonian of degree four.

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