13 citations · 42 across the 14 of their papers we have counts for
16 papers
Rotation number of 2-interval piecewise affine maps
José Pedro Gaivao, Michel Laurent, Arnaldo Nogueira
We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $f_{\p}$ are parametrized by a quintupl…
Transcendence and continued fraction expansion of values of Hecke-Mahler series
Yann Bugeaud, Michel Laurent
Let and be real numbers with and irrational. We show that the Hecke-Mahler series $$ F_{θ, ρ} (z_1, z_2) = \sum_{k_1 \ge 1} \, \sum_{k_2 = 1}^{\lfloor k…
Combinatorial structure of Sturmian words and continued fraction expansions of Sturmian numbers
Yann Bugeaud, Michel Laurent
Let be the continued fraction expansion of an irrational real number . It is well-known that the characteristic Sturmian word of slope is…
On the Diophantine nature of the elements of Cantor sets arising in the dynamics of contracted rotations
Yann Bugeaud, Dong Han Kim, Michel Laurent +1
We prove that these Cantor sets are made up of transcendental numbers, apart from their endpoints and , under some arithmetical assumptions on the data. To that purpose, we…
Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series
Michel Laurent, Arnaldo Nogueira
Let be a -interval piecewise affine increasing map which is injective but not surjective. Such a map has a rotation number and can be parametriz…
Rotation number of interval contracted rotations
Michel Laurent, Arnaldo Nogueira
Let . We consider the one-parameter family of circle -affine contractions , where . Let be the rotation num…