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On Hausdorff dimension for attractors of iterated function systems

Published online by Cambridge University Press:  09 April 2009

Qinghe Yin
Qinghe Yin
Affiliation:
School of Mathematics, The University of New South Wales, Po Box 1, Kensington, N.S.W. 2033, Australia
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Abstract

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A conjecture on the Hausdorff dimension for Markov attractors of disjoint hyperbolic iterated function systems was given by Ellis and Branton. This paper proves the conjecture and generalizes the result to more general cases.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 2 , October 1993 , pp. 216 - 231
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Bandt, C., ‘Self-similar sets 3. Constructions with sofic systems’, Mh. Math. 108 (1989), 89–102.CrossRefGoogle Scholar
[2]Ellis, D. B. and Branton, M. G., Non-self-similar attractors of hyperbolic iterated function systems, Lecture Notes in Mathematics 1342 (Springer, Berlin, 1988) pp. 158–171.Google Scholar
[3]Feiste, U., ‘A generalization of mixed invariant sets’, Mathematika 35 (1988), 198–206.CrossRefGoogle Scholar
[4]Gantmacher, F. R., The theory of matrices, volume 2 (Chelsea, 1959).Google Scholar
[5]Hutchinson, J. E., ‘Fractals and self similarity’, Indiana Univ. Math. J. 30 (1981), 713–747.CrossRefGoogle Scholar
[6]Keesling, J., ‘Hausdorff dimension’, Topology Proc. 11 (1986), 349–383.Google Scholar