Quadratic approximation to automatic continued fractions Sur l’approximation quadratique des fractions continues automatiques
نویسنده
چکیده
We study the sets of values taken by the exponents of quadratic approximation w2 and w ∗ 2 evaluated at real numbers whose sequence of partial quotients is generated by a finite automaton. Among other results, we show that these sets contain every sufficiently large rational number and also some transcendental numbers. Résumé. Nous étudions les ensembles des valeurs prises par les exposants d’approximation quadratique w2 et w ∗ 2 évalués aux nombres réels dont la suite des quotients partiels est engendrée par un automate fini. Entre autres résultats, nous montrons que ces ensembles contiennent tout nombre rationnel suffisamment grand et également des nombres transcendants.
منابع مشابه
Diophantine Approximation on Veech
— We show that Y. Cheung’s general Z-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates in an ...
متن کاملContinued Fractions , Comparison Algorithms , and Fine
There are known algorithms based on continued fractions for comparing fractions and for determining the sign of 2x2 determinants. The analysis of such extremely simple algorithms leads to an incursion into a surprising variety of domains. We take the reader through a light tour of dynamical systems (symbolic dynamics), number theory (continued fractions), special functions (multiple zeta values...
متن کاملMultipoint Schur’s algorithm, rational orthogonal functions, asymptotic properties and Schur rational approximation
In [20] the connections between the Schur algorithm, the Wall’s continued fractions and the orthogonal polynomials are revisited and used to establish some nice convergence properties of the sequence of Schur functions associated with a Schur function. In this report, we generalize some of Krushchev’s results to the case of a multipoint Schur algorithm, that is a Schur algorithm where all the i...
متن کاملA ] 9 O ct 1 99 5 Compact Jacobi matrices : from Stieltjes to Krein and M ( a , b )
In a note at the end of his paper Recherches sur les fractions continues, Stieltjes gave a necessary and sufficient condition when a continued fraction is represented by a meromorphic function. This result is related to the study of compact Jacobi matrices. We indicate how this notion was developped and used since Stieltjes, with special attention to the results by M.G. Krein. We also pay atten...
متن کاملContinued Fraction Algorithms, Functional Operators, and Structure Constants Continued Fraction Algorithms, Functional Operators, and Structure Constants 1 Continued Fraction Algorithms, Functional Operators, and Structure Constants
Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2-dimensional generalization. This paper surveys the main properties of functional operators, |transfer operators| due to Ruelle and Mayer (also following L evy, Kuzmin, Wirsing, Hensley, and others) that describe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014