Dynamics of the heat semigroup in Jacobi analysis

TL;DR

This paper investigates the chaotic and hypercyclic properties of semigroups generated by perturbations of the Jacobi Laplacian on L^p spaces, contributing to the understanding of operator dynamics in Jacobi analysis.

Contribution

It introduces new results on the chaotic and hypercyclic behavior of semigroups generated by Jacobi Laplacian perturbations, expanding operator dynamics in Jacobi analysis.

Findings

Identification of conditions for chaos in Jacobi semigroups

Characterization of hypercyclic behavior in perturbed Jacobi operators

Extension of operator dynamics theory to Jacobi analysis context

Abstract

Let $\Delta$ be the Jacobi Laplacian. We study the chaotic and hypercyclic behaviour of the strongly continuous semigroups of operators generated by perturbations of $\Delta$ with a multiple of the identity on $L^p$ spaces.