Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 515-535

ON THE DIMENSIONS OF SECTIONS FOR THE GRAPH-DIRECTED SETS

Zhi-Ying Wen and Li-Feng Xi

Tsinghua University, Department of Mathematics
10084, Beijing, P.R. China; wenzy 'at' tsinghua.edu.cn

Zhejiang Wanli University, Institute of Mathematics
315100, Ningbo, Zhejiang, P.R. China; xilifengningbo 'at' yahoo.com

Abstract. The various dimensions of the intersections of the graph-directed sets {K_i}^l_i=1 \subset Rⁿ with (n - m)-planes V + a_i (a_i \in V^\bot) were investigated for H^m almost all parameters a_i \in V^\bot satisfying (V + a_i) \cap K_i \neq \varnothing, where V \subset Rⁿ is a fixed (n - m)-dimensional subspace and V^\bot its orthogonal complement. We obtain the typical value of dimensions of sections for typical directions V and also provide a weaker result for exceptional directions.

2000 Mathematics Subject Classification: Primary 28A80.

Key words: Graph-directed set, dimension, plane section.

Reference to this article: Z.-Y. Wen and L.-F. Xi: On the dimensions of sections for the graph-directed sets. Ann. Acad. Sci. Fenn. Math. 35 (2010), 515-535.

Full document as PDF file

doi:10.5186/aasfm.2010.3532