Colloquium

The algebraic degree of a rational map $f:\mathbf{P}^n -> \mathbf{P}^n$ on complex projective space is the common degree of its homogeneous components.   The sequence $(\mathrm{deg}\, f^n)$ always grows like a power $\lambda^n $ of some number  $\lambda >= 1$.   In this talk I will discuss the significance of this dynamical degree and how one might compute it in various situations.  My final aim, however, is to describe recent work with Jason Bell and Mattias Jonsson in which we exhibit a specific example in which the first dynamical degree turns out to be (provably) a transcendental number. 

MC 5501