Parametric Lyapunov exponents
Dynamical Systems
2020-12-09 v1 Complex Variables
Abstract
In an algebraic family of rational maps of , we show that, for almost every parameter for the trace of the bifurcation current of a marked critical value, the critical value is Collet-Eckmann. This extends previous results of Graczyk and \'{S}wi\c{a}tek in the unicritical family, using Makarov theorem. Our methods are based instead on ideas of laminar currents theory.
Keywords
Cite
@article{arxiv.2003.14355,
title = {Parametric Lyapunov exponents},
author = {Henry De Thélin and Thomas Gauthier and Gabriel Vigny},
journal= {arXiv preprint arXiv:2003.14355},
year = {2020}
}