Hall 123

Some arithmetic properties of dynamical systems

Ajay Ranganathan

University of Paris VI

Given a number field \mathbb{K} and a rational function \phi : \mathbb{P}^k(\mathbb{K}) \longrightarrow \mathbb{P}^k(\mathbb{K}) ,one can study the points which are
periodic for the dynamical system defined by \phi.After an introduction giving all the vocabulary of dynamics needed, we will see that one can construct a measure on \mathbb{P}^k(\mathbb{C}) giving such information. We will also see that one can define a notion of canonical height which vanish on preperiodic points,and has a link with the canonical measure. People knowing the theory of elliptic curves and the Neron-Tate height will see some similarities.