Polynomial skew products whose Julia sets have infinitely many symmetries

TL;DR

This paper classifies polynomial skew products in complex two-dimensional space whose Julia sets possess infinitely many symmetries, expanding understanding of symmetry properties in complex dynamics.

Contribution

It provides a complete classification of polynomial skew products with Julia sets that have infinitely many symmetries, a novel result in complex dynamics.

Findings

Classified polynomial skew products with infinitely symmetric Julia sets

Identified conditions for Julia set symmetries in C^2

Enhanced understanding of symmetry structures in complex dynamical systems

Abstract

We consider the symmetries of Julia sets of polynomial skew products on C^2, which are birationally conjugate to rotational products. Our main results give the classification of the polynomial skew products whose Julia sets have infinitely many symmetries.