  This article studies the sequence of iterative degrees of a birational map of
the plane. This sequence is known either to be bounded or to have a linear,
quadratic or exponential growth. The classification elements of infinite order
with a bounded sequence of degrees is achieved, the case of elements of finite
order being already known. The coefficients of the linear and quadratic growth
are then described, and related to geometrical properties of the map. The
dynamical number of base-points is also studied. Applications of our results
are the description of embeddings of the Baumslag-Solitar groups and GL(2,Q)
into the Cremona group.
