Limit theorems for toral translations
Dmitry Dolgopyat, Bassam Fayad
TL;DR
This paper reviews classical and recent results on the statistical behavior of ergodic sums in toral translations, exploring their implications for Diophantine approximation and quasi-periodic dynamical systems.
Contribution
It synthesizes known results and open problems on ergodic sums in toral translations, highlighting their applications to various areas of dynamical systems and number theory.
Findings
Discussion of classical and recent results
Open problems in the field
Applications to Diophantine approximation
Abstract
We discuss some classical and recent results and open problems on the statistical behavior of ergodic sums above toral translations, and their applications to Diophantine approximations and to ergodic properties of systems related to quasi-periodic dynamics such as skew products, cylindrical cascades and special flows.
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 · Stochastic processes and statistical mechanics · advanced mathematical theories