Take the 2-minute tour ×  The following question is more of a
request for pointers to suitable literature on introductory
material for arithmetic dynamics and dynamics on moduli spaces.
In my dissertation, I have been working mostly with smooth
dynamical systems, and a lot with a class of dynamical systems
given by iteration of certain polynomial maps on smooth two-
dimensional (in fact algebraic) submanifolds of $\mathbb{R}^3$.
Naturally I have also been looking at holomorphic dynamics. At
some point I started to ask questions (not related to my current
work) about those dynamical systems, which seem to be better
formulated in the algebraic context, rather than analytic,
measure-theoretic or differential-geometric (all of which I am
familiar with). As a result I discovered a field (which seems to
be actively developing) of arithmetic dynamics and (somewhat
related but not entirely, I guess) dynamics on moduli spaces. I
have searched the internet for some introductory material, only
to find that literature is