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"Translations surfaces and their geodesics" by Jean-Christophe Yoccoz

In a rectangular billiard with no friction, orbits are either periodic or equidistributed. The study of such billiards is very related to the study of rotations on a circle. In general, the study of the dynamics of a polygonal billiard table whose angles are commensurable to \pi leads to fascinating dynamical objects (interval exchanges) and geometrical objects (translation surfaces). We shall try to give an overview of this topic.

Billiards

Plenary talk

BilliardsISSMYSLyon2012.pdf — PDF document, 367 KB (376679 bytes)

Afternoon talk

ISSMYS_part2.pdf — PDF document, 371 KB (380055 bytes)