#### 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.

Done