Hypercyclic abelian semigroups of affine maps on C^n

TL;DR

This paper characterizes hypercyclic abelian semigroups of affine maps on complex n-space, providing explicit criteria for finitely generated cases and showing limitations on dense orbits.

Contribution

It offers a new characterization of hypercyclic abelian semigroups of affine maps and proves that certain groups cannot have dense orbits.

Findings

No abelian group generated by n affine maps on C^n has a dense orbit.

Explicit characterization for finitely generated semigroups.

Provides conditions for hypercyclicity in affine map semigroups.

Abstract

We give a characterization of hypercyclic abelian semigroup G of affine maps on C^n. If G is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by n affine maps on C^n has a dense orbit.