On a degenerating limit theorem of DeMarco--Faber
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910285767376896 |
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| author | Okuyama, Yûsuke |
| author_facet | Okuyama, Yûsuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_14252 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On a degenerating limit theorem of DeMarco--Faber Okuyama, Yûsuke Algebraic Geometry Complex Variables Number Theory 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. |
| title | On a degenerating limit theorem of DeMarco--Faber |
| topic | Algebraic Geometry Complex Variables Number Theory |
| url | https://arxiv.org/abs/2003.14252 |