Abstract:
 Let f be a rational mapping on complex projective space. The
complexity of f as a dynamical system is measured by the dynamical
degrees. I will define the dynamical degrees and show how to compute
them in certain cases. Recently, for maps defined over the algebraic
numbers, Silverman defined numerical invariants such as the arithmetic
degree and canonical height. Arithmetic degree measures the local
arithmetic complexity of an orbit. I will also introduce the
arithmetic degree and canonical height, and present various results
and conjectures along this direction.
