Orbit portraits in non-autonomous iteration
Document Type
Article
Date of Original Version
1-1-2019
Abstract
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.
Publication Title, e.g., Journal
Discrete and Continuous Dynamical Systems - Series S
Volume
13
Issue
2
Citation/Publisher Attribution
Comerford, Mark, and Todd Woodard. "Orbit portraits in non-autonomous iteration." Discrete and Continuous Dynamical Systems - Series S 13, 2 (2019): 2253-2277. doi: 10.3934/dcdss.2019144.