Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

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 (Unpublished)

[img]
Preview
PDF (strathprints013423.pdf)
strathprints013423.pdf

Download (286kB) | Preview

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.