23 citations · 64 across the 18 of their papers we have counts for
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math.DS2011
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,…
math.DS2011★ 2 cited
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…
math.DS2011★ 1 cited
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…