### Mathematics Colloquium

# Daniel Meyer

### (Jacobs University)

## "Invariant Peano curves of expanding Thurston maps"

** Date: ** |
Mon, February 7, 2011 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:** A Thurston map is a postcritically finite branched covering map f: S^2 -> S^2. We consider such maps that are expanding in a suitable sense. We show that a suitable iterate F = f^n is semiconjugate to z^d: S^1 -> S^1. This means that there is a Peano curve g: S^1 ->S^2 (onto) such that F(g(z)) =g(z^d), where d = deg F. This generalizes a result by Milnor and corresponds to a result by Cannon-Thurston in the group case.