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

Abstract

Let $(a_n)_{n=0}^\infty$ 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 $(a_{n+1}/a_{n})_{n=0}^\infty$ in $\mathbb{Q}_p$.