**Update: the question has now been asked on the main site - Applications of number theory in dynamical systems**

I am considering asking a reference-request type question on MO about significant and/or recent applications of number theory in dynamical systems/nonlinear dynamics. I see possible overlap with arithmetic dynamics (interesting in its own right - see https://arxiv.org/abs/1806.04980 for recent progress), but I am angling more at traditional dynamical systems theory.

Note that Lagarias writes in The Unreasonable Effectiveness of Number Theory, Proceedings of Symposia in Applied Mathematics, Volume 46, 1992, American Mathematical Society in the Chapter *Number Theory and Dynamical Systems*: "Number theoretic problems have occurred repeatedly in dynamical systems". Is this still true in the last twenty years or so? (In the question itself, I could summarize or at least list some topics, including small divisors, continued fractions, Farey sequences, Diophantine approximation, etc.)

Would the above be appropriate on MO? If not, how could the question be improved to make it suitable, if possible?

*Proposed GRP 2019.08.24.*

I am looking for references (or ways to find references) on significant and/or recent applications of techniques in number theory to problems in the areas of dynamical systems and nonlinear dynamics. While there may be overlap with arithmetic dynamics ([add your arxiv example here]), I want examples leaning more towards traditional dynamical systems.

[Add the paragraph on Lagarias's remarks here, followed by] A citation search using this reference was unrewarding. Other nonrecent papers which might yield a successful citation search would be welcome. Also useful search terms would be accepted.

The Unreasonable Effectiveness of Number Theory, but it dates back to 1991/1992. $\endgroup$ – J W Aug 20 at 14:18includingby users who think your question on dynamical systems would be unsuitable for MO. If they think that, they can write it as a comment/answer. $\endgroup$ – Tom Leinster Aug 20 at 18:27