On the periodicity of an algorithm for p-adic continued fractions

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

The Euclidean algorithm and finite continued fractions

Fowler [22] Measure theory of continued fractions: Einsiedler and Ward [19, Chapter 3] and Iosifescu and Kraaikamp [35, Chapter 1]. In harmonic analysis and dynamical systems, we usually care about infinite continued fractions because we usually care about the Lebesgue measure of a set defined by some conditions on the convergents or partial quotients of a continued fraction. For some questions...