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Generalized Staircases: Recurrence and Symmetry

W. Patrick Hooper, Barak Weiss (2012)

Annales de l’institut Fourier

We study infinite translation surfaces which are -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Generalized Whitney partitions

Michał Rams (2000)

Fundamenta Mathematicae

We prove that the upper Minkowski dimension of a compact set Λ is equal to the convergence exponent of any packing of the complement of Λ with polyhedra of size not smaller than a constant multiple of their distance from Λ.

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