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10 papers · 2 filters
Weak local rules for planar octagonal tilings
Nicolas Bédaride, Thomas Fernique
We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities,…
Thermodynamic formalism and Substitutions
Nicolas Bedaride, Pascal Hubert, Renaud Leplaideur
This paper studies properties of a Renormalization Operator for potentials in symbolic dynamics. These operators first appeared in \cite{BLL} and the link with substitutions was do…
Circle averages and disjointness in typical flat surfaces on every Teichmueller disc
Jon Chaika, Pascal Hubert
We prove that on the typical translation surface the flow in almost every pair of directions are not isomorphic to each other and are in fact disjoint. It was not known if there we…
A classification of postcritically finite Newton maps
Russell Lodge, Yauhen Mikulich, Dierk Schleicher
The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some ap…
On the Hausdorf Dimension of Minimal Interval Exchange Transformations with Flips
Alexandra Skripchenko, Serge Troubetzkoy
We prove linear upper and lower bounds for the Hausdorff dimension set of minimal interval exchange transformations with flips (in particular without periodic points), and a linear…
On some symmetric multidimensional continued fraction algorithms
Pierre Arnoux, Sébastien Labbé
We compute explicitly the density of the invariant measure for the Reverse algorithm which is absolutely continuous with respect to Lebesgue measure, using a method proposed by Arn…