From order to chaos - Pisa 2018

poster: Mixing via shearing in parabolic flows

speaker: Davide Ravotti (Universität Wien)

abstract: Unipotent flows are classical examples of parabolic flows, namely flows for which the divergence of nearby points is polynomial in time. Very little is known about the ergodic properties of general smooth parabolic flows, even for smooth perturbations of homogeneous ones. We will show how a common geometric shearing mechanism can be exploited to prove mixing for three families of smooth parabolic flows, namely locally Hamiltonian flows on surfaces, time-changes of quasi-abelian filiform nilflows, and some central perturbations of unipotent flows in SL(3,R).

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