A framework for frequently occurring non-generic degeneracies

Abstract eng:
The occurrence of generic degeneracies in physical systems is closely related to underlying symmetries of the governing equations. The occurrence of additional non-generic degeneracies which cannot be accounted for by symmetry arguments is usually termed accidental. In this work, we develop a framework that helps identify and investigate a particular class of degeneracies associated with equivariant systems under certain common symmetry groups. We show that the existence of a first-integral for such systems (i.e., a potential function or energy functional) guarantees generically that non-generic degeneracies in the spectrum of the Jacobian (and other system properties) occur. We describe concrete examples of physical systems exhibiting these types of degeneracies and comment on the ramifications.

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