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Iterated function systems of finite type and the weak separation property
Author(s):
Nhu
Nguyen
Journal:
Proc. Amer. Math. Soc.
130
(2002),
483-487.
MSC (1991):
Primary 28A78;
Secondary 28A80
Posted:
May 25, 2001
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Abstract:
We prove that any iterated function system of finite type possesses the weak separation property.
References:
-
- [F]
- K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, Wiley 1990. MR 92j:28008
- [H]
- J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30(1981), 713-747. MR 82h:49026
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- S.P. Lalley,
 -expansions with deleted digits for Pisot numbers, Trans. Amer. Math. Soc. 349(1997), 4355-4365. MR 98f:11084 - [LN]
- K. Lau and S. Ngai, Multifractal measure and a weak separation condition, Adv. in Math. 141(1999), 45-96. MR 2000d:28010
- [NW]
- S. Ngai and Y. Wang, Hausdorff dimension of self-similar sets with overlaps, J. London Math. Soc., to appear.
- [Z]
- M.P.W. Zerner, Weak separation property for self-similar sets, Proc. Amer. Math. Soc. 124(1996), 3529-3539. MR 97c:54035
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Additional Information:
Nhu
Nguyen
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001 and Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam
Email:
nnguyen@nmsu.edu
DOI:
10.1090/S0002-9939-01-06063-4
PII:
S 0002-9939(01)06063-4
Keywords:
Hausdorff dimension,
open set condition,
weak separation property,
finite type condition,
iterated function system
Received by editor(s):
February 5, 2000
Received by editor(s) in revised form:
July 1, 2000
Posted:
May 25, 2001
Additional Notes:
This author has previously published as Nguyen To Nhu.
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
2001,
American Mathematical Society
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