Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 109-119

SELF-AFFINE SETS IN ANALYTIC CURVES AND ALGEBRAIC SURFACES

De-Jun Feng and Antti Käenmäki

The Chinese University of Hong Kong, Department of Mathematics
Shatin, Hong Kong; djfeng 'at' math.cuhk.edu.hk

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; antti.kaenmaki 'at' jyu.fi

Abstract. We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces do not contain non-trivial self-affine sets.

2010 Mathematics Subject Classification: Primary 28A80; Secondary 32C25, 51H30.

Key words: Self-affine set, analytic curve, algebraic surface.

Reference to this article: D.-J. Feng and A. Käenmäki: Self-affine sets in analytic curves and algebraic surfaces. Ann. Acad. Sci. Fenn. Math. 43 (2018), 109-119.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4306