Rescaling limits of complex rational maps

Abstract

We discuss rescaling limits for sequences of complex rational maps in one variable which approach infinity in parameter space. It is shown that any given sequence of maps of degree $d\ge 2$ has at most $2d-2$ dynamically distinct rescaling limits which are not postcritically finite. For quadratic rational maps, a complete description of the possible rescaling limits is given. These results are obtained by employing tools from nonarchimedean dynamics.