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Normal Forms and Unfoldings of Linear Systems in Eigenspaces of (Anti)-Automorphisms of Order Two

I. Hoveijn·J. S. W. Lamb·R. M. Roberts
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Abstract

In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and Hamiltonian, which have both time-preserving and time-reversing symmetries. However the theory gives a uniform method to obtain normal forms and unfoldings for a wide variety of linear differential equations with additional structure. We give several examples and include a discussion of the phenomenon of orbit splitting. As a consequence of orbit splitting we observe passing and splitting of eigenvalues in unfoldings.

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I. Hoveijn, J. S. W. Lamb, R. M. Roberts. 2002-10-19. Normal Forms and Unfoldings of Linear Systems in Eigenspaces of (Anti)-Automorphisms of Order Two. https://arxiv.org/abs/math/0210305

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