A Non-Autonomous Model for Parabolic Implosion
Complex Variables
2026-01-26 v1 Dynamical Systems
Abstract
Orthogonal polynomials appear naturally in the study of compositions of M\"obius transformations. In this paper, we consider several classes of orthogonal polynomials associated to non-autonomous perturbations of a parabolic M\"obius map. Our results can be viewed as instances of non-autonomous parabolic implosion, including a random perturbative regime in which convergence holds almost surely.
Cite
@article{arxiv.2601.16311,
title = {A Non-Autonomous Model for Parabolic Implosion},
author = {Katelynn Huneycutt and Samantha Sandberg-Clark and Liz Vivas},
journal= {arXiv preprint arXiv:2601.16311},
year = {2026}
}