26 citations · 62 across the 12 of their papers we have counts for
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math.DS2012
Complexity as a homeomorphism invariant for tiling spaces
Antoine Julien
It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically e…
math.DS2012
Combinatorics and topology of the Robinson tiling
Franz Gähler, Antoine Julien, Jean Savinien
We study the space of all tilings which can be obtained using the Robinson tiles (this is a two-dimensional subshift of finite type). We prove that it has a unique minimal subshift…
math.GN2012★ 4 cited
Bi-Lipshitz Embedding of Ultrametric Cantor Sets into Euclidean Spaces
Jean V. Bellissard, Antoine Julien
An ultrametric Cantor set can be seen as the boundary of a rooted weighted tree called the Michon tree. The notion of Assouad dimension is re-interpreted as seen on the Michon tree…