2020
DOI: 10.48550/arxiv.2007.06430
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The Hausdorff dimension of self-projective sets

Argyrios Christodoulou,
Natalia Jurga

Abstract: Given a finite set A ⊆ SL(2, R) we study the dimension of the attractor KA of the iterated function system induced by the projective action of A. In particular, we generalise a recent result of Solomyak and Takahashi by showing that the Hausdorff dimension of KA is given by the minimum of 1 and the critical exponent, under the assumption that A satisfies certain discreteness conditions and a Diophantine property. Our approach combines techniques from the theories of iterated function systems and Möbius semigro… Show more

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