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

Krzysztof Barański

doi:10.3934/dcds.2008.21.1015

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2008, Volume 21, Issue 4: 1015-1023. Doi: 10.3934/dcds.2008.21.1015

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

Krzysztof Barański^1,

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

Received: July 31, 2007

Revised: December 31, 2007

Published: September 2008

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Abstract

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.

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Mathematics Subject Classification: Primary 28A80, 28A78.

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