Multifractal analysis of the growth rate of digits in Schneider's p-adic continued fraction dynamical system

Let Zₚ be the ring of p-adic integers and aₙ (x) be the n-th digit of Schneider's p-adic continued fraction of x pZₚ. We study the growth rate of the digits \aₙ (x) \₍₁ from the viewpoint of multifractal analysis. The Hausdorff dimension of the set _ () =\x pZₚ: \ ₍aₙ (x) { (n) =1\}\ is completely determined for any: N^+ satisfying (n) as n. As an application, we also calculate the Hausdorff dimension of the intersection sets ^_ (, ₁, ₂) =\x pZₚ: ₍aₙ (x) { (n) =₁, ~₍aₙ (x) (n) =₂\}\ for the above function and 0₁<₂.