Iterated function systems with a weak separation condition

• Autorzy: Ka-Sing Lau , Xiang-Yang Wang
• Języki publikacji: EN

Abstrakty

EN

Nonoverlapping contractive self-similar iterated function systems (IFS) have been studied in great detail via the open set condition. On the other hand much less is known about IFS with overlaps. To deal with such systems, a weak separation condition (WSC) has been introduced recently [LN1]; it is weaker than the open set condition and it includes many important overlapping cases. This paper has two purposes. First, we consider the class of self-similar measures generated by such IFS; we give a necessary and sufficient condition for the self-similar measures to be absolutely continuous with respect to Hausdorff measures. This extends a result in [LNR]. As most of the known examples of the WSC involve algebraic integers (e.g., the golden ratio, integral dilation matrices) and the contraction ratios are equal, our second goal is to give new examples of self-similar IFS with the WSC and with more arbitrary contraction ratios.

Kategorie tematyczne

• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 161
• Numer: 3
• Strony: 249-268

Daty

wydano

2004

Twórcy

autor

Ka-Sing Lau

• Department of Mathematics, The Chinese University of Hong Kong, H.K.

autor

Xiang-Yang Wang

• Department of Mathematics, The Chinese University of Hong Kong, H.K.
• School of Mathematics and Computational Science, Zhong-Shan University, Guang-Zhou 510275, P.R. China

Identyfikatory

DOI

10.4064/sm161-3-3