23 citations · 64 across the 18 of their papers we have counts for
5 papers · 1 filter
Inhomogeneous approximation with coprime integers and lattice orbits
Michel Laurent, Arnaldo Nogueira
We obtain variants of the classical Minkowski Theorem on inhomogeneous approximation where we require moreover that the solutions be coprime integers. We link the subject wi…
Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transfomations
Tomasz Miernowski, Arnaldo Nogueira
The two-dimensional homogeneous Euclidean algorithm is the central motivation for the definition of the classical multidimensional continued fraction algorithms, as Jacobi-Perron,…
Absorbing sets of homogeneous subtractive algorithms
Tomasz Miernowski, Arnaldo Nogueira
We consider homogeneous multidimensional continued fraction algorithms, in particular a family of maps which was introduced by F. Schweiger. We prove his conjecture regarding the e…
Orbit structure of interval exchange transformations with flip
Arnaldo Nogueira, Benito Pires, Serge Troubetzkoy
A sharp bound on the number of invariant components of an interval exchange transformation is provided. More precisely, it is proved that the number of periodic components n_per an…
Continued fractions for complex numbers and values of binary quadratic forms
S. G. Dani, Arnaldo Nogueira
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex numbe…