Projections of Periodic Functions and Mode Interactions

Sofia S. B. S. D. Castro, Isabel S. Labouriau, Juliane F. Oliveira

Published 2017-03-30Version 1

We study solutions of bifurcation problems with periodic boundary conditions, with periods in an $n+1$-dimensional lattice and their projection into $n$-dimensional space through integration of the last variable. We show that generically the projection of a single mode solution is a mode interaction. This can be applied to the study of black-eye patterns.