Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^2

TL;DR

This paper explores the relationship between postcritical sets and saddle basic sets in Axiom A polynomial skew products on C^2, providing characterizations of accumulation sets and presenting a new higher degree example.

Contribution

It characterizes properties of accumulation sets in terms of saddle basic sets and introduces a novel higher degree example for Axiom A polynomial skew products.

Findings

Characterization of accumulation sets via saddle basic sets

New example of higher degree polynomial skew product

Insights into postcritical behaviors in complex dynamics

Abstract

Investigating the link between postcritical behaviors and the relations of saddle basic sets for Axiom A polynomial skew products on C^2, we characterize various properties concerning the three kinds of accumulation sets defined by DeMarco and Hruska in terms of the saddle basic sets. We also give a new example of higher degree.