$p$-adic continued fractions of Liouville type

P -adic Continued Fractions

Continued fractions in R have a single definition and algorithms for approximating them are well known. There also exists a well known result which states that √ m, m ∈ Q, always has a periodic continued fraction representation. In Qp, the field of p-adics, however, there are competing and non-equivalent definitions of continued fractions and no single algorithm exists which always produces a p...

P-adic Continued Fractions and a P-adic Behavior of Quasi-periodic Dynamical Systems

In this paper we introduce p-adic continued fractions and its application to quasi-periodic dynamical systems. Investigating the recurrent properties of its orbits, we use the lattice theory, which has direct applications to cryptography. At last we show some numerical calculations of p-adic continued fractions and Gauss reduction algorithm by using the open source software Sage.

S - adic expansions related to continued fractions

We consider S-adic expansions associated with continued fraction algorithms, where an S-adic expansion corresponds to an infinite composition of substitutions. Recall that a substitution is a morphism of the free monoid. We focus in particular on the substitutions associated with regular continued fractions (Sturmian substitutions), and with Arnoux–Rauzy, Brun, and Jacobi–Perron (multidimension...

p-Adic Egyptian Fractions

A nim-type game and continued fractions

In the two-person nim-type game called Euclid a position consists of a pair (a, b) of positive integers. Players alternate moves, a move consisting of decreasing the larger number in the current position by any positive multiple of the smaller number, as long as the result remains positive. The first player unable to make a move loses. In the restricted version a set of natural numbers Λ is giv...