关键词: Cantor triadic set, generlized Moran set, multifractal decomposition, poit-wise dimension

Abstract:

Let C be the Cantor triadic set and let C_\alpha=C+\alpha={\beta+\alpha:\beta(-C} for  -1<=\alpha<=1.Let Hp={\alpha(-C:dim|H(C_\alpha \intersection C)=(1-p)log2/log3},0<p<1.The author give the dimesions of C_\aplha intersection C and H_p. In addition the characteristic of H_p is describled by means of some measure \mu surrported on C.

Key words: Cantor triadic set, generlized Moran set, multifractal decomposition, poit-wise dimension