Abstract:
A result due to A. Avila, G. Levin, P. Makienko independently states:
Given a rational map R, if a critical point c of R is summable,
that is the Poincare series \sum 1/DR^k(c) is absolutely convergent to a non zero value,
then the rational map R is not structurally stable.
In this work we investigate the non-summable case.