CRM: Centro De Giorgi
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From order to chaos - Pisa 2018

Shearing properties and disjointness in Arnold flows

speaker: Corinna Ulcigrai (University of Bristol)

abstract: Shearing is key phenomenon in the study of parabolic systems. Quantitative shearing properties were for example used by Marina Ratner and many others to study fine spectral properties of horocycle flows (such disjointness and joining rigidity). We define a new disjointness criterion based on a quantitative form of shearing and show that it can be applied to study other smooth parabolic flows, in particular to prove disjointness properties in a class of Arnold flows (locally Hamiltonian flows on tori). As a corollary, this also proves some instances of Sarnak conjecture on M\"obius orthogonality. This is joint work with Adam Kanigowski and Mariusz Lema{\'n}czyk.

Thu 12 Apr, 16:00 - 16:50, Aula Dini
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