Experimental Mathematics

On the dimensions of certain incommensurably constructed sets

B. D. Stošić and J. J. P. Veerman


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.

Article information

Experiment. Math., Volume 9, Issue 3 (2000), 413-423.

First available in Project Euclid: 18 February 2003

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37C45: Dimension theory of dynamical systems
Secondary: 28A80: Fractals [See also 37Fxx]


Veerman, J. J. P.; Stošić, B. D. On the dimensions of certain incommensurably constructed sets. Experiment. Math. 9 (2000), no. 3, 413--423. https://projecteuclid.org/euclid.em/1045604676

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