For more information about this meeting, contact Dmitri Burago, Anatole Katok.

Title: | Uncertainty Principle and Traps for Polygonal Billiards |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Gregory Galperin, Eastern Illinois University |

Abstract: |

A generic billiard trajectory when being reflected from a finite set of disjoint mirror segments on the plane eventually goes to infinity; exceptions, in all known cases, are periodic trajectories. A long-standing question was: Is this the only class of possible exceptions?
For example, if the segments are parts of the sides of a simply connected polygon (“polygonal segments”), then only periodic billiard orbits can be trapped by these segments (Galperin, Krueger, Troubetskoy). For such set of segments there is a theorem on finiteness of the orbit types, and some interesting upper bounds can be found. Under some natural restrictions, a uniform upper bound can be established (Delman, Galperin). The former result is based on the so-called Uncertainty Principle for Polygons that will be considered in the talk.
The speaker will also show examples of “non-periodic traps” in the case of “non-polygonal mirror segments” on the plane. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 04 / 13 / 2011 |

Time: | 03:35pm - 05:30pm |