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Lyapunov exponents and bifurcation current for polynomial-like maps

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arxiv math/0512557 v1 pith:ZGUAXLOH submitted 2005-12-24 math.DS math.CV

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classification math.DSmath.CV
keywords bifurcationexponentslyapunovmapspolynomial-likecontinuitycurrentcurrents
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We study holomorphic families of polynomial-like maps depending on a parameter s. We prove that the partial sums of largest Lyapunov exponents are plurisubharmonic functions of s. We also study their continuity and introduce the bifurcation locus as the support of bifurcation currents.

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  1. Genus and Gonality of Small Curves, Dynamical Uniform Boundedness, and Bifurcation

    math.DS 2026-07 unverdicted novelty 8.0 of 10

    Gonality of distinct dynatomic curves tends to infinity for non-isotrivial one-parameter rational-map families on P^1, with superlinear genus growth outside flexible Lattès families.

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