Tony Samuel

Dixmier traces and coarse multifractal analysis

We show how multifractal properties of a measure supported by a fractal F ⊆ [0, 1] may be expressed in terms of complementary intervals of F and thus in terms of spectral triples and the Dixmier trace of certain operators. For self-similar measures this leads to a noncommutative integral over F equivalent to integration with respect to an auxilary multifractal measure.

ON THE CONVERGENCE TO EQUILIBRIUM OF UNBOUNDED OBSERVABLES UNDER A FAMILY OF INTERMITTENT INTERVAL MAPS

We consider a family

On the asymptotics of the

{\{T_{r}: [0, 1] \circlearrowleft \}_{r\in[0, 1]}}

-Farey transfer operator

{Tr:[0,1]↺}r∈[0,1] of Markov interval maps interpolating between the tent map

Regularity of aperiodic minimal subshifts

{T_{0}}

A classification of aperiodic order via spectral metrics and Jarník sets

T0 and the Farey map