The measure of maximal entropy extends continuously to resolution compactifications of the parameter and moduli spaces of rational maps, answering a question of DeMarco.
Non-Archimedean techniques and dynamical degenerations
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abstract
We develop non-Archimedean techniques to analyze the degeneration of a sequence of rational maps of the complex projective line. We provide an alternative to Luo's method which was based on ultra-limits of the hyperbolic 3-space. We build hybrid spaces using Berkovich theory which enable us to prove the convergence of equilibrium measures, and to determine the asymptotics of Lyapunov exponents.
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Compactifications and measures for rational maps
The measure of maximal entropy extends continuously to resolution compactifications of the parameter and moduli spaces of rational maps, answering a question of DeMarco.