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Errata to ‘Hausdorff dimension for horseshoes’

Published online by Cambridge University Press:  19 September 2008

Anthony Manning
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.

Type
Errata
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 319
Copyright
Copyright © Cambridge University Press 1985