Invariance of Poincare-Lyapunov Polynomials Under the Group of Rotations

Date

1998-10-09

Authors

Joyal, Pierre

Journal Title

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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. <i>Electronic Journal of Differential Equations, 1998</i>(23), pp. 1-8.

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Attribution 4.0 International

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