Hypercyclic Abelian Affine Groups
Adlene Ayadi
TL;DR
This paper characterizes hypercyclic abelian affine groups, providing explicit criteria for finitely generated cases and showing that certain groups cannot have dense orbits in complex n-space.
Contribution
It offers a complete characterization of hypercyclic abelian affine groups and proves a non-existence result for groups generated by n affine maps on C^n.
Findings
Explicit characterization for finitely generated groups
No abelian group generated by n affine maps on C^n has a dense orbit
Provides conditions for hypercyclicity in affine groups
Abstract
In this paper, we give a characterization of hypercyclic abelian affine group G. 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · advanced mathematical theories · Coding theory and cryptography