CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici Olomorfi 2018-2019

seminar: Spectral disjointness of rescaling of some surface flows

speaker: Przemysław Berk (Nicolaus Copernicus University)

abstract: We are interested relation of some surface flows with their rational rescalings. In a recent paper 1 Kanigowski, Lemańczyk and Ulcigrai proved that different real rescalings of a special flow built over rotation and under roof function with asymmetric logarithmic singularities are disjoint in the sense of Furstenberg. We proof analogous result for roof function with symmetric singularities and only for rational rescalings, we replace however Furstenberg disjointness by spectral disjointness. While in 1 authors relied on properties of Ratner type, we present different approach. Moreover, by using similar methods, we show that special flows built over IETs and under piecewise linear functions (with both zero and non-zero slope) satisfy identical property. It is partially generalization of results by Frączek and Lemańczyk in 2. All mentioned special flows arise naturally as special representations of flows on surfaces.

Tue 2 Apr, 10:00 - 11:00, Sala Conferenze Centro De Giorgi
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