Boundary parametrization of self-affine tiles

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概要

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• 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.

• 社団法人 日本数学会の論文

著者

• Akiyama Shigeki

  Department of Mathematical Science, Graduate School of Science and Technbology, Niigata University

• Loridant Benoît

  Montanuniversität Leoben, Lehrstuhl für Mathematik und Statistik

関連論文

• The Selberg trace formula for modular correspondences
• Boundary parametrization of self-affine tiles
• Boundary parametrization of self-affine tiles

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