Residual Transitivity implies Minimality for Markoff Surfaces over $p$-adic Integers, by Means of $p$-adic Flows

Seung Uk Jang

Let $X_D^{\ast }$ be the non-singuar locus of the Markoff surface $X_D:x^2+y^2+z^2=xyz+D$ and consider the set of its $p$-adic integer points $X_D^{\ast }({\mathbb{Z}}_p)$. It is kno…