Título inglés |
Quasiconformal dimensions of self-similar fractals. |
Título español |
Dimensiones cuasiconformes de fractales autosemejantes. |
Autor/es |
Tyson, Jeremy T. ; Wu, Jang-Mei |
Organización |
Dep. Math. Univ. Illinois, Urbana (Illinois), Estados Unidos |
Revista |
0213-2230 |
Publicación |
2006, 22 (1): 205-258, 29 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
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. |
Clasificación UNESCO |
120209 ; 120217 |
Palabras clave español |
Aplicaciones cuasiconformes ; Dimensión de Hausdorff ; Fractales ; Sistemas de funciones iteradas |
Código MathReviews |
MR2268118 |
Código Z-Math |
Zbl 1108.30015 |
Acceso al artículo completo |