Are there some researches about the next dynamical system: x'=Z(x) where Z is the classical Riemann zeta function? The equation is deffined in R^2\{1} and x'=||x-1||^2 Z(x) is an equivalent formulation. Riemann zeta is pretty important and a system like this may be studied by someone, right?
Ricardo Egydio De Carvalho
Zeta function has connection with "quantum chaos". Look at the papers:
http://www.bourbaphy.fr/keating.pdf
https://pdfs.semanticscholar.org/3918/ff44ab4f1e885cdaa84d1b907f693c0d6314.pdf?_ga=1.224330845.736023740.1487860643
and the previous references cited therein.
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Jason Bramburger
Not sure if it completely addresses your question, but I immediately thought of this paper: http://www.sciencedirect.com/science/article/pii/S0022314X14002868
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