5. Generalization of Complex Dynamical Results to Higher Dimensions

Problem 5.1.
[H. Krieger, C. Petsche] What is the bifurcation measure $\mu_{\rm{bif}}$ in $\mathcal{M}_d^N$ (over a field $\Bbb{C}_\nu$)? 
Problem 5.2.
[L. DeMarco] Is a dynamically stable algebraic family of degree $d$ maps $\Bbb{CP}^N\rightarrow\Bbb{CP}^N$ (i.e. a subvariety of ${\rm{End}}^N_d$) which is not Lattès or isotrivial necessarily PCF? 
Problem 5.3.
[J. Silverman] Selfsimilarity of $p$adic bifurcation loci in $1$parameter families when $p<\text{ the degree}$?
Remark. How about $p$adic analogues of Tan Lei’s result on the similarity of the Mandelbrot set to a Julia set near certain points?

Remark. Related, the family $\left\{z^3\frac{3}{2}tz^2\right\}_{t\to 1\, (2\text{adically})}$ is studied by J. Anderson.

Cite this as: AimPL: Moduli spaces for algebraic dynamical systems, available at http://aimpl.org/modalgdyn.