Relatório de pesquisa 16/09

Reversal Symmetries for Planar Vector Fields, A. Algaba, C. García and M. A. Teixeira, submitted June 02, 2009.

In this paper, we formulate a comprehensive study of  relevant properties of reversible vector fields. As a consequence, we prove that the reversibility of the first non-zero quasi-homogeneous term, respect to some types, of a vector field is a necessary condition for the reversibility of the vector  field. We also provide a straightforward characterization of the reversibility for  quasi-homogeneous vector fields. Finally, as an application of our previous results, we analyze some special polynomial and nilpotent systems, including examples which are centers and non-reversible.

Mathematics Subject Classifications (2000):  


Copy of the file:

rp16-09.pdf (PDF)

June 02, 2009


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