Parametric Lyapunov exponents
Copyright policy )Parametric Lyapunov exponents
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 Świcatek in the unicritical family, using Makarov theorem. Our methods are based instead on ideas of laminar currents theory.
Mathematics - Complex Variables, [MATH] Mathematics [math], Dynamical Systems (math.DS), laminar currents theory, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets, rational maps, Currents, FOS: Mathematics, 28D20, 37F45, 37F10, Makarov theorem, [MATH]Mathematics [math], Mathematics - Dynamical Systems, Complex Variables (math.CV)
Mathematics - Complex Variables, [MATH] Mathematics [math], Dynamical Systems (math.DS), laminar currents theory, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets, rational maps, Currents, FOS: Mathematics, 28D20, 37F45, 37F10, Makarov theorem, [MATH]Mathematics [math], Mathematics - Dynamical Systems, Complex Variables (math.CV)
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