The Dynamical Degrees of a Mapping

Let f be a rational mapping of a space X . The complexity of (f,X) as a dynamical system is measured by the dynamical degrees ${\delta }_p(f)$, $1\le p\le {\rm dim}(X)$. We give the definition of the dynamical degrees show how they are computed in certain cases. For instance, we show that if the dynamical degree of an automorphism of a K"ahler manifold is greater than one, then it must be irrational.