Seminari di Fisica Matematica
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| Seminari A.A. 2019-2020 |
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Relatore |
Titolo |
Data |
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Christoph Lehner
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17 dicembre 2019 |
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Chiara Boccato
IST Austria |
12 novembre 2019 |
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Maxime Hauray
Univeristé Aix-Marseille |
05 novembre 2019 |
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Nguyen Tong Xuan
GSSI L'Aquila |
28 ottobre 2019 (lunedì) |
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Sara Daneri
GSSI L'Aquila |
22 ottobre 2019 |
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Horst Knörrer
ETH Zürich |
15 ottobre 2019 |
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Abstract ritorna |
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.
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