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arXiv · 2003.14355

Parametric Lyapunov exponents

Henry De Thélin·Thomas Gauthier·Gabriel Vigny
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Abstract

In an algebraic family of rational maps of $\mathbb{P}^1$, 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.

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Henry De Thélin, Thomas Gauthier, Gabriel Vigny. 2020-03-30. Parametric Lyapunov exponents. https://doi.org/10.1112/blms.12441

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