Jordan, Thomas, Pollicott, Mark and Simon, Karoly. (2007) Hausdorff dimension for randomly perturbed self affine attractors. Communications in Mathematical Physics, Vol.270 (No.2). pp. 519-544. ISSN 0010-3616

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Abstract

In this paper we shall consider a self-affine iterated function system in R-d, d >= 2, where we allow a small random translation at each application of the contractions. We compute the dimension of a typical attractor of the resulting random iterated function system, complementing a famous deterministic result of Falconer, which necessarily requires restrictions on the norms of the contraction. However, our result has the advantage that we do not need to impose any additional assumptions on the norms. This is of benefit in practical applications, where such perturbations would correspond to the effect of random noise. We also give analogous results for the dimension of ergodic measures ( in terms of their Lyapunov dimension). Finally, we apply our method to a problem originating in the theory of fractal image compression.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Communications in Mathematical Physics
Publisher:	Springer
ISSN:	0010-3616
Date:	March 2007
Volume:	Vol.270
Number:	No.2
Number of Pages:	26
Page Range:	pp. 519-544
Identification Number:	10.1007/s00220-006-0161-7
Status:	Not Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/32508

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