Nous étudions une classe de suites symboliques, les codages de rotations, intervenant dans des problèmes de répartition des suites et représentant une généralisation géométrique des suites sturmiennes. Nous montrons que ces suites peuvent être obtenues par itération de quatre substitutions définies sur un alphabet à trois lettres, puis en appliquant un morphisme de projection. L’ordre d’itération de ces applications est gouverné par un développement bi-dimensionnel de type “fraction continue”...
We consider subshifts arising from primitive substitutions, which are known to be
uniquely ergodic dynamical systems. In order to precise this point, we introduce a
symbolic notion of discrepancy. We show how the distribution of such a subshift is in
part ruled by the spectrum of the incidence matrices associated with the underlying
substitution. We also give some applications of these results in connection with the
spectral study of substitutive dynamical systems.
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.
There is a long tradition in constructing explicit classes of transcendental continued fractions and especially transcendental continued fractions with bounded partial quotients. By means
of the Schmidt Subspace Theorem, existing results were recently substantially improved by the authors in a series of papers, providing new classes of transcendental continued fractions. It is the purpose of the present work to show how the Quantitative Subspace Theorem yields transcendence measures for (most of)...
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
The main purpose of this work is to present new families of transcendental continued fractions with bounded partial quotients. Our results are derived thanks to combinatorial transcendence criteria recently obtained by the first two authors in [3].
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