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5. Generalization of Complex Dynamical Results to Higher Dimensions

    1. 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?
            1. Remark. Known for $N=1$ [MR890160].
                • Problem 5.3.

                  [J. Silverman] Self-similarity of $p$-adic bifurcation loci in $1$-parameter families when $p<\text{ the degree}$?
                    1. 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.