Hausdorff dimension of self-affine limit sets with an invariant direction

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November 2008, 21(4): 1015-1023. doi: 10.3934/dcds.2008.21.1015

Hausdorff dimension of self-affine limit sets with an invariant direction

1.	Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland

Received August 2007 Revised January 2008 Published May 2008

Abstract
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We determine the Hausdorff dimension of self-affine limit sets for some class of iterated function systems in the plane with an invariant direction. In particular, the method applies to some type of generalized non-self-similar Sierpiński triangles. This partially answers a question asked by Falconer and Lammering and extends a result by Lalley and Gatzouras.

Keywords: fractal, Hausdorff dimension, Iterated Function System., Sierpiński triangle.

Mathematics Subject Classification: Primary 28A80, 28A7.

Citation: Krzysztof Barański. Hausdorff dimension of self-affine limit sets with an invariant direction. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1015-1023. doi: 10.3934/dcds.2008.21.1015

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