Article ID Journal Published Year Pages File Type
1890770 Chaos, Solitons & Fractals 2006 10 Pages PDF
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].
Related Topics
Physical Sciences and Engineering Physics and Astronomy Statistical and Nonlinear Physics
Preview
Dimension of invariant sets for mappings with the squeezing property
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