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arXiv · 1211.0927

Dimension results for inhomogeneous Moran set constructions

Mark Holland·Yiwei Zhang
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Abstract

We compute the Hausdorff, upper box and packing dimensions for certain inhomogeneous Moran set constructions. These constructions are beyond the classical theory of iterated function systems, as different nonlinear contraction transformations are applied at each step. Moreover, we also allow the contractions to be weakly conformal and consider situations where the contraction rates have an infimum of zero. In addition, the basic sets of the construction are allowed to have a complicated topology such as having fractal boundaries. Using techniques from thermodynamic formalism we calculate the fractal dimension of the limit set of the construction. As a main application we consider dimension results for stochastic inhomogeneous Moran set constructions, where chaotic dynamical systems are used to control the contraction factors at each step of the construction.

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Mark Holland, Yiwei Zhang. 2012-11-13. Dimension results for inhomogeneous Moran set constructions. https://arxiv.org/abs/1211.0927

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