Type: Article
Publication Date: 2016-07-04
Citations: 8
DOI: https://doi.org/10.1007/s40993-016-0041-y
Let K be a complete, algebraically closed non-Archimedean valued field, and let $$\varphi (z) \in K(z)$$ have degree two. We describe the crucial set of $$\varphi $$ in terms of the multipliers of $$\varphi $$ at the classical fixed points, and use this to show that the crucial set determines a stratification of the moduli space $$\mathcal {M}_2(K)$$ related to the reduction type of $$\varphi $$ . We apply this to settle a special case of a conjecture of Hsia regarding the density of repelling periodic points in the classical non-Archimedean Julia set.