Analysis Seminar

Joaco Prandi, University of Waterloo

When the weak separation condition implies the generalize finite type in R^d

Let S be an iterated function system with full support. Under some restrictions on the allowable rotations, we will show that S satisfies the weak separation condition if and only if it satisfies the generalized finite-type condition. To do this, we will extend the notion of net intervals from R to R^d. If time allows, we will also use net intervals to calculate the local dimension of a self-similar measure with the finite-type condition and full support.

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