Seminari del Dipartimento


Fisica Matematica

On the BKL conjectures - Oscillatory singular, spatially homogenuous space times

Prof. H. Knoerrer

15-10-2019 - 14:30
Largo San Leonardo Murialdo,1 - Pal.C - Aula 311


The vacuum Einstein equations for Bianchi space times (that is space times that can be foliated into three dimensional space like slices that are all homogenuous spaces) reduce to a system of ordinary differential equations.
The conjectures of Belinskii, Khalatnikov and Lifshitz predict that for almost all initial data the solutions of these differential equation behave like trajectories of a billiard in a Farey triangle in the hyperbolic plane, that is, a triangle whose three vertices are ideal points. In joint work with M.Reiterer and E.Trubowitz we show that, for a set of initial data that has positive measure, this is indeed the case.   
We use ideas inspired by scattering theory for approximations of the system.
The fact that billiard in a Farey triangle is chaotic leads us to small divisor problems similar to those of KAM theory in Hamiltonian dynamics. 
org: GIULIANI Alessandro

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