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2000 On the dimensions of certain incommensurably constructed sets
J. J. P. Veerman, B. D. Stošić
Experiment. Math. 9(3): 413-423 (2000).

Abstract

It is known that the Hausdorff dimension of the invariant set $\Lambda_t$ of an iterated function system ${\cal F}_t$ on $\R^n$ depending smoothly on a parameter $t$ varies lower-semicontinuously, but not necessarily continuously. For a specific family of systems we investigate numerically the conjecture that discontinuities in the dimension only arise when in some iterate of the iterated function system two or more branches coincide. This happens in a dense set of codimension one. All other points are conjectured to be points of continuity.

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J. J. P. Veerman. B. D. Stošić. "On the dimensions of certain incommensurably constructed sets." Experiment. Math. 9 (3) 413 - 423, 2000.

Information

Published: 2000
First available in Project Euclid: 18 February 2003

zbMATH: 0996.37022
MathSciNet: MR1795313

Subjects:
Primary: 37C45
Secondary: 28A80

Rights: Copyright © 2000 A K Peters, Ltd.

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Vol.9 • No. 3 • 2000
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