For more information about this meeting, contact Stephen Simpson.

Title: | Topological pressure for non-compact sets, Kamae entropy and Kolmogorov complexity |

Seminar: | Logic Seminar |

Speaker: | Daniel Thompson, Pennsylvania State University |

Abstract: |

For compact spaces, the theory of topological pressure and equilibrium states is a cornerstone of modern ergodic theory. It has long been thought desirable to generalize this theory to non-compact spaces. I will give a brief over-view of the various approaches to this problem in the literature and give an elementary alternative definition of topological pressure in the non-compact setting. It turns out that this definition is a generalization of the Kamae entropy. The definition assigns a non-negative number to each point in the space and can be interpreted as a sort of complexity. In Cantor space, this quantity is related to the Kolmogorov complexity. I will attempt to give an accessible explanation of the dynamical systems context of this theory. I will then describe some results by Brudno, Kamae, Van Lambalgen and White to illustrate the connection with Kolmogorov complexity and to demonstrate why this may be of interest to Logicians. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 11 / 30 / 2010 |

Time: | 02:30pm - 03:45pm |