6 citations · 18 across the 7 of their papers we have counts for
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The aperiodic complexities and connections to dimensions and Diophantine approximation
Viktor Schroeder, Steffen Weil
In their earlier work (Ergodic Th. Dynam. Sys., 34: 1699 -1723, 10 2014), the authors introduced the so called F-aperiodic orbits of a dynamical system on a compact metric space X,…
Diophantine approximations for translation surfaces and planar resonant sets
Luca Marchese, Rodrigo Treviño, Steffen Weil
We consider Teichmüller geodesics in strata of translation surfaces. We prove lower and upper bounds for the Hausdorff dimension of the set of parameters generating a geodesic boun…
Dimension Functions on the Spectrum over Bounded Geodesics and Applications to Diophantine Approximation
Steffen Weil
The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are k…
Jarnik-type Inequalities
Steffen Weil
It is well known due to Jarnik that the set Bad of badly approximable numbers is of Hausdorff-dimension one. If Bad(c) denotes the subset of x in Bad for which the approximation co…
Schmidt Games and Conditions on Resonant Sets
Steffen Weil
Winning sets of Schmidt's game enjoy a remarkable rigidity. Therefore, this game (and modifications of it) have been applied to many examples of complete metric spaces (X, d) to sh…
Aperiodic Sequences and Aperiodic Geodesics
Viktor Schroeder, Steffen Weil
We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on c…