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

Title: | Algebraic independence of multipliers of two periodic orbits in the space of polynomials of degree greater or equal than three |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Igor Gorbovickis, Cornell University |

Abstract: |

Let $P_d$ be the space of monic polynomials of degree $d\ge 3$. For
any pair of distinct periodic orbits of a polynomial from $P_d$,
consider a corresponding pair of (multi valued) algebraic functions on
$P_d$, obtained by analytic continuation of the multipliers of these
orbits. In the first part of the talk we will show that these two
functions are algebraically independent.
A map is Kupka-Smale if all its periodic points are hyperbolic and the
stable and unstable manifolds of any two saddle points are transverse.
In the second part of the talk we will show, how the result from the
first part is used in the proof of the Kupka-Smale theorem for volume
preserving polynomial automorphisms of $\bbC^2$ of dynamical degree
$d\ge 3$. Roughly speaking, the theorem says that a typical volume
preserving polynomial automorphisms of $\bbC^2$ of dynamical degree
$d\ge 3$ is Kupka-Smale. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 03 / 26 / 2012 |

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