Kepler Sets of Second-Order Linear Recurrence Sequences Over ${\mathbb{Q}}_p$

Let $(a_n{)}_{n=0}^{\mathrm{\infty }}$ be a second-order linear recurrence sequence with constant coefficients over the field of $p$-adic numbers ${\mathbb{Q}}_p$. We study the set of limit points of the sequence of consecutive ratios $(a_{n+1}\mathrm{/}{a}_n{)}_{n=0}^{\mathrm{\infty }}$ in ${\mathbb{Q}}_p$.