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A topological separation condition for fractal attractors

Bedford, Tim and Borodachov, S. and Geronimo, J. (2010) A topological separation condition for fractal attractors. UNSPECIFIED. (Unpublished)

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    Abstract

    We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundant on every level. In general this separation condition is weaker than the strong open set condition and is not equivalent to the weak separation property. We prove that this separation condition is equivalent to the strong Markov property (see definition below). We also show that the set of N-tuples of contractive homeomorphisms, which are non-redundant on every level, is a G set in the topology of pointwise convergence of every component mapping with an additional requirement that the supremum of contraction coefficients of mappings be strictly less than one. We give several sufficient conditions for this separation property. For every fixed N-tuple of d×d invertible contraction matrices from a certain class, we obtain density results for N-tuples of fixed points which define N-tuples of mappings non-redundant on every level.

    Item type: Other
    ID code: 13423
    Keywords: separation condition, hausdorff dimension, similarity dimension, open set condition, markov partition property, self-similar sets, Probabilities. Mathematical statistics
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Department: Strathclyde Business School > Management Science
    Related URLs:
    Depositing user: Mrs Caroline Sisi
    Date Deposited: 16 Nov 2009 13:37
    Last modified: 27 Nov 2012 14:27
    URI: http://strathprints.strath.ac.uk/id/eprint/13423

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