An inverse problem in P\'olya--Schur theory. II. Exactly solvable operators and complex dynamics

Autor:	Alexandersson, Per, Hemmingsson, Nils, Shapiro, Boris
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems 37F10 (Primary) 34A30 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 23 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.01643 Zobrazit plný text záznamu View this record from Arxiv