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

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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.
    Mathematics Subject Classification: Primary 28A80, 28A78.


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