2006•NonlinearityRequires access

Hausdorff dimension for an open class of repellers in

Nuno Luzia

Abstract

We compute the Hausdorff dimension for an open class of iterated function schemes in in the C 2 topology, in terms of the pressure function . This class is characterized by a domination condition that is not too strong , plus the non-overlapping condition . Also in this class there exists a unique invariant probability measure of full Hausdorff dimension. Finally we show that the Hausdorff dimension is a continuous function in this class.

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Key concepts: Mathematics, Hausdorff dimension, Dimension function, Packing dimension, Urysohn and completely Hausdorff spaces, Hausdorff measure, Effective dimension, Outer measure