Representation of period doubling by digraphs and characteristic polynomials

Abstract

A general procedure which defines a partial ordering of cyclic permutations induced by continuous maps is known for constructing immediate successors to a cycle. We expound on this procedure in terms of labelled digraphs and characteristic polynomials then apply this study to period doubling, the most common route to chaos for a nonlinear dynamical system.

arXiv comment16 pages, 3 figures