Arithmetic intersection and measures of maximal entropy


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October 21, 2021 4:00 pm - 6:00 pm
Science Center 232

Laura DeMarco - Harvard University

About 10 years ago, Xinyi Yuan and Shouwu Zhang proved that if two holomorphic maps f and g on P^N have the same sets of preperiodic points (or if the intersection of Preper(f) and Preper(g) is Zariski dense in P^N), then they must have the same measure of maximal entropy.  This was new even in dimension N=1.  I will describe some ingredients in their proof, while emphasizing the dynamical history behind this result.  I will also sketch the proof of a theorem of Levin and Przytycki from the 1990s, in dimension N=1, that two (non-exceptional) maps have the same measure of maximal entropy if and only if they "essentially" share an iterate.

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