English

Parametric Lyapunov exponents

Dynamical Systems 2020-12-09 v1 Complex Variables

Abstract

In an algebraic family of rational maps of P1\mathbb{P}^1, 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}
}
R2 v1 2026-06-23T14:34:08.130Z