There is a well established multifractal theory for self-similar measures generated by non-overlapping contractive similutudes. Our report here concerns those with overlaps. In particular we restrict our at...There is a well established multifractal theory for self-similar measures generated by non-overlapping contractive similutudes. Our report here concerns those with overlaps. In particular we restrict our attention to the important classes of self-similar measures that have matrix representations. The dimension spectra and the L q -spectra are analyzed through the product of matrices. There are abnormal behaviors on the multifractal structure and they will be discussed in detail.展开更多
文摘There is a well established multifractal theory for self-similar measures generated by non-overlapping contractive similutudes. Our report here concerns those with overlaps. In particular we restrict our attention to the important classes of self-similar measures that have matrix representations. The dimension spectra and the L q -spectra are analyzed through the product of matrices. There are abnormal behaviors on the multifractal structure and they will be discussed in detail.
