Divergent diagrams of folds and simultaneous conjugacy of involutions - Mancini, S.; Manoel, M.; Teixeira, M. A. (Amer Inst Mathematical Sciences, 2005)
In this work we show that the smooth classification of divergent diagrams of folds (f(1),..., f(s)) : (R-n, 0) -> (R-n x(...)xR(n), 0) can be reduced to the classification of the s-tuples (p(1)., W) of associated involutions. We apply the result to obtain normal forms when s <= n and {p(1),...,p(s)} is a transversal set of linear involutions. A complete description is given when s = 2 and n >= 2. We also present a brief discussion on applications of our results to the study of discontinuous vector fields and discrete reversible dynamical systems.
Keywords: divergent diagram of folds; involution; singularities; normal form; discontinuous vector fields; reversible diffeomorphisms