A model for the parabolic slices Per_1(e^{2\pi i p/q}) in moduli space of quadratic rational maps

TL;DR

This paper introduces relatedness loci in parabolic slices of quadratic rational maps, providing a model for their structure and a proof strategy for its accuracy, enhancing understanding of these complex dynamical systems.

Contribution

It presents a new model for relatedness loci in parabolic slices of quadratic rational maps and outlines a proof strategy for its faithfulness.

Findings

The relatedness loci are analogous to the disconnectedness locus in polynomial slices.

A concrete model for these loci is proposed.

A proof strategy for the model's faithfulness is outlined.

Abstract

The notion of relatedness loci in the parabolic slices Per_1(e^{2\pi i p/q}) in moduli space of quadratic rational maps is introduced. They are counterparts of the disconnectedness or escape locus in the slice of quadratic polynomials. A model for these loci is presented, and a strategy of proof of the faithfulness of the model is given.