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9 papers · 2 filters
Regular simplices and periodic billiard orbits
Nicolas Bedaride, Michael Rao
A simplex is the convex hull of points in which form an affine basis. A regular simplex is a simplex with sides of the same length. We consider the bil…
Herman's condition and critical points on the boundary of Siegel disks of polynomials with two critical values
Arnaud Chéritat, Pascale Roesch
We extend a theorem of Herman from the case of unicritical polynomials to the case of polynomials with two finite critical values. This theorem states that Siegel disks of such pol…
An algorithm to identify automorphisms which arise from self-induced interval exchange transformations
Yann Jullian
We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transform…
Diffusion for the periodic wind-tree model
Vincent Delecroix, Pascal Hubert, Samuel Lelièvre
The periodic wind-tree model is an infinite billiard in the plane with identical rectangular scatterers disposed at each integer point. We prove that independently of the size of t…
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…