Algebraic dynamics, function fields and descent

Algebraic dynamics is the study of dynamical systems defined by rational maps on algebraic varieties. One of its themes consists in interpreting questions and (sometimes) theorems from classical Diophantine geometry as instances of questions for general algebraic dynamical systems. In the first part of these notes, we give a rapid introduction to this circle of ideas. We then focus on the determination of “limited orbits” for algebraic dynamical systems over function dields. In the last part we explain the statement of the proof of