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arXiv · 2601.16311

A Non-Autonomous Model for Parabolic Implosion

Katelynn Huneycutt·Samantha Sandberg-Clark·Liz Vivas
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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.

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Katelynn Huneycutt, Samantha Sandberg-Clark, Liz Vivas. 2026-01-22. A Non-Autonomous Model for Parabolic Implosion. https://arxiv.org/abs/2601.16311

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