INVESTIGADORES
PANZONE Pablo Andres
artículos
Título:
On the measure of self-similar sets II
Autor/es:
PANZONE PABLO A.
Revista:
REVISTA DE LA UNIóN MATEMáTICA ARGENTINA
Editorial:
UNION MATEMATICA ARGENTINA
Referencias:
Lugar: Bahia Blanca; Año: 1996 vol. 40 p. 83 - 100
ISSN:
0041-6932
Resumen:
Summary: “In §1 we show a condition forHs(Kb) > 0 for almost all b = (b1, · · · , bl) 2 Rnl, whereKb =Sli=1  i(Kb) and  i are similitudes,  i(x):Rn !Rn defined by  i(x) = kiAix+bi, Ai anorthogonal matrix, 0 < ki < 13, bi a vector ofRn. In §2 we give a (geometric) criterion for a setK = Sli=1  i(K) to have Hs(K) = 0 if the Hausdorff dimension is equal to its similarity dimension.In §3 we develop a method for calculating the measure ofK =Sli=1  i(K) whenK meets certainconditions, generalizing a method shown in Part I of this paper [Rev. Un. Mat. Argentina 38(1992), no. 1-2, 48–87 (1993); MR1276016 (94m:28015)]. We also calculate dimensions of setsK such that their dimensions do not coincide with their similarity dimensions. Finally, we givesome examples (Sierpi´nski sets with overlapping).”