Invariance of Poincare-Lyapunov Polynomials Under the Group of Rotations
Date
1998-10-09
Authors
Joyal, Pierre
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We show that the Poincaré-Lyapunov polynomials at a focus of a family of real polynomial vector fields of degree n on the plane are invariant under the group of rotations. Furthermore, we show that under the multiplicative group ℂ* = {ρe iψ}, they are invariant up to a positive factor. These results follow from the weighted-homogeneity of the polynomials that we define in the text.
Description
Keywords
focus, invariance of Poincare-Lyapunov polynomials, weighted-homogeneity
Citation
Joyal, P. (1998). Invariance of Poincare-Lyapunov polynomials under the group of rotations. Electronic Journal of Differential Equations, 1998(23), pp. 1-8.
Rights
Attribution 4.0 International