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Dimension of invariant sets for mappings with the squeezing property |
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| Authors: | Andrzej Lasota Janusz Traple |
| Affiliation: | aInstitute of Mathematics, Silesian University, and Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland bInstitute of Computer Sciences, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland |
| 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]. |
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