Boundary parametrization and the topology of tiles

Shigeki Akiyama, Benoit Loridant

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As an application of the boundary parametrization developed in our previous papers, we propose a new method to deduce information on the connected components of the interior of tiles. This gives a systematic way to study the topology of a certain class of self-affine tiles. An example due to Bandt and Gelbrich is examined to prove the efficiency of the method.
Original languageEnglish
Pages (from-to)127-164
Number of pages38
JournalNagoya Mathematical Journal
Issue numberJune
Publication statusE-pub ahead of print - 19 Oct 2016

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