Continued fractions without fractions: Lagrange theorem and Pell equations Original Research Article

Quadratic irrationals and their representation as continued fractions are investigated by means of proper tools of Discrete Dynamical Systems theory. This is done by recasting the process of generation of digits in the continued fraction expansion of a real number as a suitable discrete nonlinear system whose asymptotic behavior is to be studied. Such an approach allows, on the one hand, to retrieve well known results in the literature, the most relevant being the Lagrange theorem, and on the other hand it aims to give more insight into some related issues.