The Hausdorff dimension of the Smale-Williams solenoid with different contraction coefficients
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- Proc. Amer. Math. Soc. 125 (1997), 1221-1228 Request permission
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 $\frac {\log 2}{\log (1/\max (\lambda ,\mu ))}$.References
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Additional Information
- Károly Simon
- Affiliation: Institute of Mathematics, University of Miskolc, H-3515 Miskolc, Hungary
- MR Author ID: 250279
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1221-1228
- MSC (1991): Primary 58F12; Secondary 58F15
- DOI: https://doi.org/10.1090/S0002-9939-97-03600-9
- MathSciNet review: 1350964