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Thickness measures for Cantor sets


Author: S. Astels
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 108-111
MSC (1991): Primary 58F12; Secondary 28A78
DOI: https://doi.org/10.1090/S1079-6762-99-00068-2
Published electronically: July 20, 1999
MathSciNet review: 1701889
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Abstract: For a fixed $k\ge 1$ let $C_1,\dots,C_k$ be generalized Cantor sets. We examine various criteria under which $C_1+\dots + C_k$ contains an interval. When these criteria do not hold, we give a lower bound for the Hausdorff dimension of $C_1+\dots+C_k$. Our work will involve the development of two different types of thickness measures.


References [Enhancements On Off] (What's this?)

  • 1. S. Astels. Cantor sets and numbers with restricted partial quotients, Trans. Amer. Math. Soc. (to appear).
  • 2. Thomas W. Cusick and Mary E. Flahive. The Markoff and Lagrange spectra, Amer. Math. Soc., Providence, RI, 1989. MR 90i:11069
  • 3. Sheldon E. Newhouse. The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 101-151. MR 82e:58067
  • 4. J. Palis and F. Takens. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, Cambridge, 1993. MR 94h:58129

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Additional Information

S. Astels
Affiliation: Department of Pure Mathematics, The University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: sastels@barrow.uwaterloo.ca

DOI: https://doi.org/10.1090/S1079-6762-99-00068-2
Keywords: Cantor sets, sums of sets, Hausdorff dimension
Received by editor(s): March 15, 1999
Published electronically: July 20, 1999
Additional Notes: Research supported in part by the Natural Sciences and Engineering Research Council of Canada.
Communicated by: Yitzhak Katznelson
Article copyright: © Copyright 1999 American Mathematical Society

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