### Inhomogeneous Kaufman measures and diophantine approximation

Ergodic Theory and Dynamical Systems Seminar

19th October 2023, 2:00 pm – 3:00 pm

Fry Building, G.07

Kaufman constructed a family of Rajchman measures on the set of badly approximable numbers. Pollington and Velani used these to show that Littlewood’s conjecture holds for a full-dimensional set of pairs of badly approximable numbers. We construct analogous measures that have implications for inhomogeneous diophantine approximation. In joint work with Agamemnon Zafeiropoulos and Evgeniy Zorin, our idea is to shift the continued fraction and Ostrowski expansions simultaneously.

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