A DICHOTOMY OF STRONG OPEN SET CONDITION OF SELF-CONFORMAL SETS

摘要

Let K be a C1+alpha self-conformal set. It is well known that K satisfies the strong open set condition provided it satisfies the open set condition. A point x is an element of K is called a trivial point of K if {x} is a connected component of K. Let U be a strong open set for K. In this paper, we show that whether U contains a trivial point of K determines several metrical and topological properties of K, including the maximal power law property and the dimension drop of the connected part of K.

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