On elastic graph spines associated to quadratic Thurston maps

Authors

MELİKE YETİŞER
ALİ BERKAY YETİŞER

DOI

10.55730/1300-0098.3154

Abstract

For a quadratic Thurston map having two distinct critical points and $n$ postcritical points, we count the number of possible dynamical portraits. We associate elastic graph spines to several hyperbolic quadratic Thurston rational functions. These functions have four postcritical points, real coefficients, and invariant real intervals. The elastic graph spines are constructed such that each has embedding energy less than one. These are supporting examples to Dylan Thurston's recent positive characterization of rational maps. Using the same characterization, we prove that with a combinatorial restriction on the branched covering and a cycle condition on the dynamical portrait, a quadratic Thurston map with finite postcritical set of order $n$ is combinatorially equivalent to a rational map. This is a special case of the Bernstein-Levy theorem.

Keywords

Quadratic Thurston map, branched self-cover, elastic graph spine, embedding energy

First Page

1233

Last Page

1242

Recommended Citation

YETİŞER, MELİKE and YETİŞER, ALİ BERKAY (2022) "On elastic graph spines associated to quadratic Thurston maps," Turkish Journal of Mathematics: Vol. 46: No. 4, Article 7. https://doi.org/10.55730/1300-0098.3154
Available at: https://journals.tubitak.gov.tr/math/vol46/iss4/7