Quasiconformal dimensions of self-similar fractals.

Jeremy T. Tyson; Jang-Mei Wu

Revista Matemática Iberoamericana (2006)

  • Volume: 22, Issue: 1, page 205-258
  • ISSN: 0213-2230

Abstract

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The Sierpinski gasket and other self-similar fractal subsets of Rd, d ≥ 2, can be mapped by quasiconformal self-maps of Rd onto sets of Hausdorff dimension arbitrarily close to one. In R2 we construct explicit mappings. In Rd, d ≥ 3, the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have quasisymmetrically equivalent invariant sets, and (ii) one-parameter isotopies of systems have invariant sets which are equivalent under global quasiconformal maps.

How to cite

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Tyson, Jeremy T., and Wu, Jang-Mei. "Quasiconformal dimensions of self-similar fractals.." Revista Matemática Iberoamericana 22.1 (2006): 205-258. <http://eudml.org/doc/41971>.

@article{Tyson2006,
abstract = {The Sierpinski gasket and other self-similar fractal subsets of Rd, d ≥ 2, can be mapped by quasiconformal self-maps of Rd onto sets of Hausdorff dimension arbitrarily close to one. In R2 we construct explicit mappings. In Rd, d ≥ 3, the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have quasisymmetrically equivalent invariant sets, and (ii) one-parameter isotopies of systems have invariant sets which are equivalent under global quasiconformal maps.},
author = {Tyson, Jeremy T., Wu, Jang-Mei},
journal = {Revista Matemática Iberoamericana},
keywords = {Aplicaciones cuasiconformes; Dimensión de Hausdorff; Fractales; Sistemas de funciones iteradas; quasiconformal mappings; Hausdorff dimension},
language = {eng},
number = {1},
pages = {205-258},
title = {Quasiconformal dimensions of self-similar fractals.},
url = {http://eudml.org/doc/41971},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Tyson, Jeremy T.
AU - Wu, Jang-Mei
TI - Quasiconformal dimensions of self-similar fractals.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 1
SP - 205
EP - 258
AB - The Sierpinski gasket and other self-similar fractal subsets of Rd, d ≥ 2, can be mapped by quasiconformal self-maps of Rd onto sets of Hausdorff dimension arbitrarily close to one. In R2 we construct explicit mappings. In Rd, d ≥ 3, the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have quasisymmetrically equivalent invariant sets, and (ii) one-parameter isotopies of systems have invariant sets which are equivalent under global quasiconformal maps.
LA - eng
KW - Aplicaciones cuasiconformes; Dimensión de Hausdorff; Fractales; Sistemas de funciones iteradas; quasiconformal mappings; Hausdorff dimension
UR - http://eudml.org/doc/41971
ER -

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