Relatório de pesquisa 18/09
Reversibility and Quasi-Homogeneous Normal Forms of Vector Fields, A. Algaba, C. García and M.A. Teixeira, submitted June 29, 2009.
Abstract
This paper uses tools in Quasi-Homogeneous Normal Form
theory to discuss certain aspects of reversible vector fields around an
equilibrium point. Our main result provides an algorithm, via Lie
Triangle, that detects the non-reversibility of vector fields. As a
consequence we answer an intriguing question related to the
problems derived from the $16^{\circ}$ Hilbert Problem. That is, it is
possible to decide whether a planar center is not reversible. Some of
the theory developed is also applied to get further results on
nilpotent and degenerate polynomial vector fields. We find several
families of nilpotent centers which are non-reversible.
Mathematics Subject Classifications
(2000):
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June 29, 2009
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