Factorization of the Stability Polynomials of Ring Systems

2017/05/07 by Leandro, Eduardo S. G. · 2 citations
#37Cxx #37N05 #70F10 #70Fxx #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.02701

Abstract

Let D_n be the dihedral group with 2n elements, and suppose n is greater than one. We call ring system a finite D_n-symmetric set of points in ℝ². Ring systems have been used as models for planets surrounded by rings, and may be seen as relative equilibria of the N-body or the N-vortex problem. As a first significant step towards linear stability analysis, we study the factorization of the stability polynomial of an arbitrary ring system by systematically exploiting the ring's symmetry through representation theory of finite groups. Our results generalize contributions by J. C. Maxwell from mid-XIX century until contemporary authors such as J. Palmore and R. Moeckel, among others.

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