2016/07/01 by Mark Comerford, Comerford, Mark, Todd Woodard +1
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 30D05 #Secondary 37F10 #math.CV #math.DS #msc:30D05 #msc:37F10
paper · pdf · doi:10.48550/arxiv.1607.00339
26 pages, 7 figures
arxiv created 2016/07/01 · arxiv updated 2016/07/04
We extend the definition of an orbit portrait to the context of non-autonomous iteration, both for the combinatorial version involving collections of angles and for the dynamic version involving external rays where combinatorial portraits can be realized by the dynamics associated with sequences of polynomials with suitably uniformly bounded degrees and coefficients. We show that, in the case of sequences of polynomials of constant degree, the portraits which arise are eventually periodic which is somewhat similar to the classical theory of polynomial iteration. However, if the degrees of the polynomials in the sequence are allowed to vary, one can obtain portraits with complementary arcs of irrational length which are fundamentally different from the classical ones.