Boundary parametrization of self-affine tiles
AKIYAMA, Shigeki ; LORIDANT, Benoît
J. Math. Soc. Japan, Tome 63 (2011) no. 2, p. 525-579 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2011-04-15
Classification:  self-affine tile,  graph directed set,  Hausdorff measure,  Büchi automata,  28A80,  52C20,  68Q70,  05B45,  28A78,  37F20,  51M20,  54D05 
@article{1303737797,
     author = {AKIYAMA, Shigeki and LORIDANT, Beno\^\i t},
     title = {Boundary parametrization of self-affine tiles},
     journal = {J. Math. Soc. Japan},
     volume = {63},
     number = {2},
     year = {2011},
     pages = { 525-579},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303737797}
}

AKIYAMA, Shigeki; LORIDANT, Benoît. Boundary parametrization of self-affine tiles. J. Math. Soc. Japan, Tome 63 (2011) no. 2, pp.  525-579. http://gdmltest.u-ga.fr/item/1303737797/