Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 803-811

C¹-EMBEDDINGS BETWEEN GRAPH-DIRECTED SETS

Juan Deng, Zhiying Wen and Lifeng Xi

ShenZhen University, Department of Mathematics
518000, ShenZhen, P.R. China; dengjuan 'at' szu.edu.cn

Tsinghua University, Department of Mathematics
100084, Beijing, P.R. China; wenzy 'at' tsinghua.edu.cn

Ningbo University, Department of Mathematics
315211, Ningbo, P.R. China; xilifengningbo 'at' yahoo.com

Abstract. For graph-directed sets, we obtain that a C¹-embedding implies an affine embedding. We only pose the open set condition for the image sets. We can apply our result to self-similar sets with overlaps, for example all λ-Cantor sets.

2010 Mathematics Subject Classification: Primary 28A80.

Key words: Fractal, graph-directed sets, embedding.

Reference to this article: J. Deng, Z. Wen and L. Xi: C¹-embeddings between graph-directed sets. Ann. Acad. Sci. Fenn. Math. 41 (2016), 803-811.

Full document as PDF file

doi:10.5186/aasfm.2016.4153

C1-EMBEDDINGS BETWEEN GRAPH-DIRECTED SETS

Juan Deng, Zhiying Wen and Lifeng Xi

C¹-EMBEDDINGS BETWEEN GRAPH-DIRECTED SETS