Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

Fourier coefficients of continuous measures on the Furstenberg sequence

Talk by Prof. Dr. Sophie Grivaux

Speaker invited by: Prof. Dr. Corinna Ulcigrai

Date: 14.10.19  Time: 14.00 - 15.00  Room: ETH HG G 43

We will present a negative answer to a conjecture of Lyons, related to Furstenberg $x2$-$x3$ conjecture, concerning the existence of a continuous probability measure on the unit circle with large Fourier coefficients on the Furstenberg set {2^p3^q ; p,q \geq 0}. The proof involves rigidity sequences for weakly mixing dynamical systems, and a generalization of a recent construction of such sequences by Fayad and Thouvenot. This is joint work with Catalin Badea.