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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Hausdorff dimension
of the Smale-Williams solenoid
with different contraction coefficients


Author: Károly Simon
Journal: Proc. Amer. Math. Soc. 125 (1997), 1221-1228
MSC (1991): Primary 58F12; Secondary 58F15
MathSciNet review: 1350964
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Abstract: In this paper we prove that the Hausdorff dimension of the Smale-Williams solenoid $\overline {\Lambda } $ with different contraction coefficients $\lambda ,\mu $ is given by the formula $\dim _H(\overline {\Lambda } )=1+\frac {\log 2}{\log (1/\max (\lambda ,\mu ))}$. Further, for $\lambda ,\mu <\frac 18$ we prove that the Hausdorff dimension of each angular section is equal to $\frac {\log 2}{\log (1/\max (\lambda ,\mu ))}$.


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Additional Information

Károly Simon
Affiliation: Institute of Mathematics, University of Miskolc, H-3515 Miskolc, Hungary

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03600-9
PII: S 0002-9939(97)03600-9
Received by editor(s): June 23, 1994
Received by editor(s) in revised form: February 27, 1995, and July 26, 1995
Additional Notes: The author was partially supported by grant F4411 from the OTKA Foundation
Communicated by: Mary Rees
Article copyright: © Copyright 1997 American Mathematical Society