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 (Unpublished)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 nonredundant 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 Ntuples of contractive homeomorphisms, which are nonredundant 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 Ntuple of d×d invertible contraction matrices from a certain class, we obtain density results for Ntuples of fixed points which define Ntuples of mappings nonredundant on every level.
Item type:  Other 

ID code:  13423 
Keywords:  separation condition, hausdorff dimension, similarity dimension, open set condition, markov partition property, selfsimilar sets, Probabilities. Mathematical statistics 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics 
Department:  Strathclyde Business School > Management Science 
Depositing user:  Mrs Caroline Sisi 
Date Deposited:  16 Nov 2009 13:37 
Last modified:  21 Jul 2015 15:07 
URI:  http://strathprints.strath.ac.uk/id/eprint/13423 
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