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 rather scarce, and I haven't been able to find a description of major problems or conjectures which are driving the field.

**Questions:**

1) What would be good references for some of the fundamental results in arithmetic dynamics?

2) What are questions of interest in arithmetic dynamics? Are there any major actively researched conjectures? What is driving the field? Are there any strong connections with well-known problems in other fields?

3) Is there any introductory literature of expository nature?

4) Questions (1) - (3) applied to dynamics on moduli spaces (I really don't know much about this field, other than the phrase "dynamics on moduli spaces" that I seem to come across often lately).

**Note:** Not sure whether I should make this a community wiki; please advise.