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.

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):  


Copy of the file:

rp18-09.pdf (PDF)

June 29, 2009


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