On a degenerating limit theorem of DeMarco--Faber

Yûsuke Okuyama

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arXiv · 2003.14252

On a degenerating limit theorem of DeMarco--Faber

Yûsuke Okuyama

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Abstract

One of our aims is to complement the proof of DeMarco--Faber's degenerating limit theorem for the family of the unique maximal entropy measures parametrized by a punctured open disk associated to a meromorphic family of rational functions on the complex projective line degenerating at the puncture. This complementation is done by our main result, which rectifies a key computation in their argument. We also establish and use a direct and explicit translation from degenerating complex dynamics into quantized Berkovich dynamics, instead of using DeMarco--Faber's more conceptual transfer principle between those dynamics.

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Yûsuke Okuyama. 2020-03-30. On a degenerating limit theorem of DeMarco--Faber. https://arxiv.org/abs/2003.14252

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