De Marco's papers are here: https://sites.math.northwestern.edu/~demarco/ and it's /the Sullivan dictionary/
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Souichiro Ikebe's site is here: http://math-functions-1.watson.jp/index_050.html#section010 … [a Misiurewicz -stalk- has a U(1)-torsor which you can perform the Droste dance with a la Lenstra: http://www.ams.org/notices/200304/fea-escher.pdf … and so there's a nice way to go from limit exact self similarity to elliptic curves]
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