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Thickness measures for Cantor sets
Author(s):
S.
Astels
Journal:
Electron. Res. Announc. Amer. Math. Soc.
5
(1999),
108-111.
MSC (1991):
Primary 58F12;
Secondary 28A78
Posted:
July 20, 1999
MathSciNet review:
1701889
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Abstract:
For a fixed  let  be generalized Cantor sets. We examine various criteria under which  contains an interval. When these criteria do not hold, we give a lower bound for the Hausdorff dimension of  . Our work will involve the development of two different types of thickness measures.
References:
- 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:
10.1090/S1079-6762-99-00068-2
PII:
S 1079-6762(99)00068-2
Keywords:
Cantor sets,
sums of sets,
Hausdorff dimension
Received by editor(s):
March 15, 1999
Posted:
July 20, 1999
Additional Notes:
Research supported in part by the Natural Sciences and Engineering Research Council of Canada.
Communicated by:
Yitzhak Katznelson
Copyright of article:
Copyright
1999,
American Mathematical Society
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