2002/10/19 by I. Hoveijn, Hoveijn, I., J. S. W. Lamb +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.math/0210305
24 pages in LaTeX, no figures. Accepted for publication in JDE
arxiv created 2002/10/19 · arxiv updated 2009/11/30
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.