Patterns of Non-Stationary Solutions to Symmetric Systems of Second-Order Differential Equations

TL;DR

This paper proves the existence of non-stationary solutions for symmetric second-order differential systems using equivariant degree theory and a new characterization of orbit types in the Burnside Ring.

Contribution

It introduces a novel approach combining equivariant degree theory with orbit type characterization for symmetric differential equations.

Findings

Existence of non-stationary solutions established.

New characterization of orbit types in Burnside Ring.

Method applicable to symmetric systems with group actions.

Abstract

We establish the existence of non-stationary solutions to a symmetric system of second-order autonomous differential equations. Our technique is based on the equivariant degree theory and involves a novel characterization of orbit types of maximal kind in the Burnside Ring product of a finite number of basic degrees for the group $O(2) \times \Gamma \times \mathbb Z_2$.