Work

An inverse problem in Pólya--Schur theory. II. Exactly solvable operators and complex dynamics

Year: 2024

Type: preprint

Abstract: This paper, being the sequel of [An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators], studies a class of linear ordinary differential operators with polynomial coefficients called \emph{exactly solvable}; such an operator sends every polynomial of sufficiently large degree to a polynomial of the same degree. We focus on invariant subsets of the complex plane for such operators when their action is restricted to polynomials of a fixed degree and discover a connection between this topic and classical complex dynamics and its multi-valued counterpart. As a very special case of invariant sets we recover the Julia sets of rational functions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2412.01643

Authors: Alexandersson, Per, Hemmingsson, Nils, Shapiro, Boris

Institution: Stockholm University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Vetenskapsrådet

Award: Differential equations and complex dynamics

OpenAlex ID: W4405034428

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