Automorphisms with exotic orbit growth
Stephan Baier, Sawian Jaidee, Shaun Stevens, Thomas Ward
TL;DR
This paper explores the growth behavior of automorphisms on one-dimensional solenoids, revealing continua with distinct growth scales in the context of the dynamical Mertens' theorem.
Contribution
It demonstrates the existence of continua with different orbit growth scales in ergodic automorphisms, highlighting complex dynamical behaviors.
Findings
Existence of continua with multiple growth scales
New insights into orbit growth in ergodic automorphisms
Connections to the dynamical Mertens' theorem
Abstract
We exhibit continua on two different growth scales in the dynamical Mertens' theorem for ergodic automorphisms of one-dimensional solenoids.
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.