V-Variable Fractals: Fractals with Partial Self Similarity

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We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.
33 pages, 3 figures

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Dynamical Systems, Probability, 28A80; 37H99; 60G57; 60J05

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http://salesiana.dossiersoluciones.com/handle/123456789/153944

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.0064
 http://arxiv.org/abs/0802.0064

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arXiv