Annales Academię Scientiarum Fennicę

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
**R**^{n} 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 **R**^{n} 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

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