Lower type dimensions of some Moran sets

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY（2019）

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摘要

In this paper, we discuss the lower type dimensions for sonic Moran sets. On one hand, for Moran set E with c(*) > 0, we prove that dim(qL) E = sup(f) dim(L) f (E), where the supremum is taken over all quasi-Lipschitz mappings f . On the other hand, we obtain the lower spectrum formula for homogeneous Moran sets. In the proof a lower spectrum formula for a large class of fractal sets is established.

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关键词

Lower Dimension,Quasi-Lower Dimension,Lower Spectrum,Quasi-Lipschitz Maping,Moran Set

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