On dimension and absolute continuity of self-similar measures

Vortrag von Constantin Kogler

Datum: 02.04.25  Zeit: 13.30 - 14.30  Raum: ETH HG G 19.1

I will present my recent joint work with Samuel Kittle. We establish numerous novel explicit examples of absolutely continuous self-similar measures. In fact, we give the first inhomogenous examples in dimension 1 and 2 and construct examples for essentially any given rotations and translations, provided they have algebraic coefficients. Moreover we strengthen Varju’s result for Bernoulli convolutions and Lindenstrauss-Varju’s result in dimension ≥ 3. We also generalise Hochman’s result to contracting on average measures and show that a separation condition weaker than exponential separation is sufficient.