Abschätzung der Periodenlänge einer verallgemeinerten Kettenbruchentwicklung.
Accumulation Points of the Lagrange and Markov Spectra.
Addendum to "Continued fractions of some algebraic numbers".
Algebraic continued fractions in and recurrent sequences in
Algorithme de Jacobi-Perron dans un corps de séries formelles
Almost-sure growth rate of generalized random Fibonacci sequences
We study the generalized random Fibonacci sequences defined by their first non-negative terms and for n≥1, Fn+2=λFn+1±Fn (linear case) and ̃Fn+2=|λ̃Fn+1±̃Fn| (non-linear case), where each ± sign is independent and either + with probability p or − with probability 1−p (0<p≤1). Our main result is that, when λ is of the form λk=2cos(π/k) for some integer k≥3, the exponential growth of Fn for 0<p≤1, and of ̃Fn for 1/k<p≤1, is almost surely positive and given by ∫0∞log x dνk, ρ(x),...
An approximation property of quadratic irrationals
Let be irrational. Several authors studied the numberswhere is a positive integer and denotes the set of all real numbers of the form with restricted integer coefficients . The value of was determined for many particular Pisot numbers and for the golden number. In this paper the value of is determined for irrational numbers , satisfying with a positive integer .
An ergodic sum related to the approximation by continued fractions.
An infinite product with bounded partial quotients
An iterated logarithm type theorem for the largest coefficient in continued fractions
Approximation by Nearest Integer Continued Fractions.
Approximation by Nearest Integer Continued Fractions (II).
Approximation of irrationals.
Approximation Properties of Jacobi's Algorithm.
Approximation Properties of Some Complex Continued Fractions.
Approximations diophantiennes des nombres sturmiens
Nous établissons pour tout nombre sturmien (de développement dyadique sturmien) des propriétés d'approximation diophantienne très précises, ne dépendant que de l'angle de la suite sturmienne, généralisant ainsi des travaux antérieurs de Ferenczi-Mauduit et Bullett-Sentenac.
Approximations simultanées de deux nombres réels
Approximations simultanées de deux séries formelles quadratiques
Arithmetic diophantine approximation for continued fractions-like maps on the interval
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.
Automatic continued fractions are transcendental or quadratic
We establish new combinatorial transcendence criteria for continued fraction expansions. Let be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients of is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.