Abstract
A standard way to parametrize the boundary of a connected fractal tile T is proposed. The parametrization is Hölder continuous from R/Z to ∂T and fixed points of ∂T have algebraic preimages. A class of planar tiles is studied in detail as sample cases and a relation with the recurrent set method by Dekking is discussed. When the tile T is a topological disk, this parametrization is a bi-Hölder homeomorphism.
Citation
Shigeki AKIYAMA. Benoît LORIDANT. "Boundary parametrization of self-affine tiles." J. Math. Soc. Japan 63 (2) 525 - 579, April, 2011. https://doi.org/10.2969/jmsj/06320525
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