Value distribution of any order derivatives in polynomial dynamics (Yûsuke Okuyama - Kyoto Institute of Technology, Japon)

For a (complex) polynomial f(z) of degree >1, the celebrated Brolin'
equidistribution theorem asserts that the averaged pullbacks
of any initial value but one exception in the complex plane under the
iterates f^n of f converges towards the harmonic measure of the Julia set of f.
In this talk, we present an (any order) derivatives version of Brolin's theorem
in an optimal form, after Gauthier--Vigny and the speaker's former works
on the first order derivatives version. This talk is based on a joint work with
Gabriel Vigny (Amiens).