Dirichlet is not just bad and singular in many rational IFS fractals
Johannes Schleischitz
Abstract:For $m\ge 2$, consider K the m-fold Cartesian product of the limit set of an iterated function system (IFS) of two affine maps with rational coefficients. If the contraction rates of the IFS are reciprocals of integers, and K does not degenerate to singleton, we construct vectors in K that lie within the ‘folklore set’ as defined by Beresnevich et al., meaning that they are Dirichlet improvable but not singular or badly approximable (in fact our examples are Liouville vectors). We further address the topic of … Show more
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