## Experimental Mathematics

### On the dimensions of certain incommensurably constructed sets

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 18 February 2003

https://projecteuclid.org/euclid.em/1045604676

Mathematical Reviews number (MathSciNet)
MR1795313

Zentralblatt MATH identifier
0996.37022

Subjects
Primary: 37C45: Dimension theory of dynamical systems

#### Citation

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