For more information about this meeting, contact Manfred Denker.

Title: | Poisson limit for two-dimensional toral automorphisms driven by a continued fraction |

Seminar: | Seminar on Probability and its Application |

Speaker: | Mikhail Gordin, POMI, St. Petersburg |

Abstract: |

We consider a sequence of hyperbolic automorphisms of the two-dimensional torus produced from a pair of irrational real numbers via their continued fraction expansions. We will sketch the proof of a Pitskel-type Poisson limit theorem for such a sequence. Powers of a single automorphism present an example of a sequence of this kind, but power sequences constitute only a countable subset of the continual set of such sequences. A construction (due to Jens Markloff) of sequences of such type against a geodesic on the upper halfplane and a fundamental domain for the action of SL(2,Z) will be explained. Approach to other probabilistic results and possible generalizaions will be briefly discussed. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 04 / 13 / 2012 |

Time: | 02:20pm - 03:20pm |