We discuss and illustrate the behaviour of the continued fraction expansion of a formal power series under specialisation of parameters or their reduction modulo p and sketch some applications of the reduction theorem here proved.

If α is an irrational number, we let {pn/qn}n≥0, be the approximants given by its continued fraction expansion. The Bruno series B(α) is defined as

We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion. In the quartic and sextic cases we observe explicitly that the parameters appearing in the continued fraction expansion yield integer sequences def...

We study the probabilistic behavior of continued fraction expansion a quadratic irrational number, when weighted by some “additive” cost. prove asymptotic Gaussian limit laws, with an optimal speed convergence. deal underlying dyn

Abstract We consider the continued fraction expansion of real numbers under action a nonuniform lattice in $\text {PSL}(2,{\mathbb R})$ and prove metric relations between convergents natural geometric notion good approximations.

In this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural ...

In this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural ...

We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algebraic numbers. One motivation is to explain the method’s good performance in practice. We improve the previously known bound by a factor of dτ , where d is the polynomial degree and τ bounds the coefficient bitsize, thu...