Electronic Research Announcements

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1079-6762

Previous volume \| Table of contents \| Next volume Articles in press \| Most recent volume \| All volumes Previous Article \| Next Article

Currently published by the American Institute of Mathematical Sciences as Electronic Research Announcements in Mathematical Sciences

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
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

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:

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

Similar Articles:

Retrieve articles in Electronic Research Announcements with MSC (1991): 58F12, 28A78

Retrieve articles in all Journals with MSC (1991): 58F12, 28A78

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


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS