Time:

14:00-15:30, on September 4

15:10-16:40, on September 11, 18 and 25

Abstract:

In this series of lectures we will investigate dynamical properties of analytic germs in dimension 2 for which the linear part at the fixed point is a contraction.

In the first lecture we will review the 1-dimensional case, and the higher dimensional invertible case.

In the second lecture, we will investigate some properties of superattracting germs (whose linear part is nilpotent) in dimension 2 or higher.

In the third lecture, we will introduce valuation spaces, as a tool to study the action induced by local dynamical systems.

In the fourth (and last) lecture, we will describe the dynamics induced by a contracting germ on valuation spaces, and deduce some properties for the original local dynamical system.