### Phase transition of capacity for uniform $G_{\delta}$ sets

Fernando Quintino
We study the capacity of a uniform $G_{\delta}$ set. Changing the speed at which the lengths of intervals generating it decrease, we observe a sharp phase transition from full to zero capacity. Such a $G_{\delta}$ set is also interesting because it can be considered as a model case for the set of exceptional energies in the parametric version of the Furstenberg theorem. In the talk, we will demonstrate the techniques used and as well as...
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