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Dimension of invariant sets for mappings with the squeezing property

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  • Lasota, Andrzej
  • Traple, Janusz

Abstract

We show an estimate of the fractal and Hausdorff dimension of sets invariant with respect to families of transformations. This estimate is proved under assumption that the transformations satisfy a squeezing property which is more general than the Lipschitz condition. Our results generalize the classical Moran formula [Moran PAP. Additive functions of intervals and Hausdorff measure. Proc Camb Philos Soc 1946;42:15–23].

Suggested Citation

  • Lasota, Andrzej & Traple, Janusz, 2006. "Dimension of invariant sets for mappings with the squeezing property," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1271-1280.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:5:p:1271-1280
    DOI: 10.1016/j.chaos.2005.08.171
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