Perturbations of weakly expanding critical orbits
Dynamical Systems
2013-09-17 v2 Complex Variables
Abstract
Let f be a polynomial or a rational function which has r summable critical points. We prove that there exists an r-dimensional manifold in an appropriate space containing f such that for every smooth curve in it through f, the ratio between parameter and dynamical derivatives along forward iterates of at least one these summable points tends to a non-zero number.
Keywords
Cite
@article{arxiv.1111.6270,
title = {Perturbations of weakly expanding critical orbits},
author = {Genadi Levin},
journal= {arXiv preprint arXiv:1111.6270},
year = {2013}
}
Comments
Extended version, to appear in the proceedings of the conference "Frontiers in complex dynamics (Celebrating John Milnor's 80th birthday)"