Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Airi Takeuchi
KIT, Karlsruhe

 
spricht am
 
Montag, 15. November 2021
 
um
 
16:15 Uhr
 
im
 
1009/L und Zoom (hybride Veranstaltung)
 
über das Thema:
 

»Conformal transformations on integrable mechanical billiards«

Abstract:
The integrability of the free billiards in the plane has been firstly studied by G. D. Birkhoff. Later, Y. G. Sinai examined their chaotic behavior and ergodicity. L. Boltzmann proposed mechanical billiard systems in the presence of a central force, and he expected such billiards with a line not passing through the center as a reflection wall to be ergodic. Recently, by Gallavotti and Jauslin, it has been shown that such billiards under the Kepler potential are actually integrable. In this talk, we explain that several integrable mechanical billiards, including Boltzmann’s integrable billiards, are connected via conformal transformations. As an application, we show that any focused conic section gives rise to integrable Kepler billiards, which can be seen as a generalization of a previous work of Gallavotti-Jauslin. We also show that any confocal conic sections give rise to integrable billiard systems of Euler’s two-center problems. This talk is based on a joint work with Lei Zhao from University of Augsburg.

If you want to take part via Zoom please ask PD Dr. Lei Zhao for­ login details.


 

Hierzu ergeht herzliche Einladung.
PD Dr. Lei Zhao
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



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