## Institute for Mathematical Sciences

## Preprint ims99-10

** J.J.P. Veerman and B. Stosic**
* On the Dimensions of Certain Incommensurably Constructed Sets*

Abstract: It is well 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 $t$ does not vary
continuously. In fact, it has been shown recently that in
general it varies lower-semi-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) of its
branches coincide. This happens in a set of co-dimension one,
but which is dense. All the other points are conjectured to be
points of continuity.

View ims99-10 (PDF format)