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Errata to ‘Hausdorff dimension for horseshoes’

Published online by Cambridge University Press:  19 September 2008

Anthony Manning
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, England
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In our paper ‘Hausdorff dimension for horseshoes’ (H. McCluskey and A. Manning, Ergod. Th. & Dynam. Sys. (1983) 3, 251–260), § 3 entitled ‘Continuity across a bifurcation’ should be deleted since the proof of theorem 3 there is wrong.

The mistake is that does not in fact imply that δs → 1. This is because, for q = q0, the function is is only non-positive rather than negative and so is not strictly decreasing function of t.(Thus the pressure curve in figure 3 may, for q = q0, have become horizontal before t = l.) A similar mistake occurs in the second half of the same proof. Thus the claim of theorem 3 that the Hausdorff dimension of the basic set changes continuously in the bifurcation from Anosov to DA remains unproved. The rest of the paper is not affected.

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Errata
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Copyright © Cambridge University Press 1985