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Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Thursday, July 15, 16:00 ~ 16:30 UTC-3

Local dimensions of self-similar measures with overlap

Kathryn Hare

University of Waterloo, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The local dimension of a measure is a way to quantify its local behaviour. For self-similar measures that satisfy a suitable separation condition, it is well known that the set of attainable local dimensions is a closed interval, but for measures which fail to satisfy this condition the situation is more complicated and less well-understood. We will show that for a large class of self-similar measures on R with ‘controlled’ overlap the set of local dimensions is a finite union of (possibly singleton) compact intervals, the number of which is bounded by geometric properties of the underlying IFS.

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