Abstract:

In this talk we will discuss the complexity of a family of birational maps. Our aim is to classify this family in order to study its dynamics.  For this purpose we have studied the most important measure of complexity of $f$ which is called its dynamical degree $D(f)=lim_{n ightarrow infty} (textrm{deg}f^{n})^{1/n}.$ We have determined $D$ for all the existing maps inside this family. We will present some examples from our work to explain the techniques (of blow up and Picard Group).

This is joint work with Anna Cima.