Exponential mixing of all orders and CLT for generic birational maps of ℙ^k

2024/02/02 by De Thélin, Henry, Vigny, Gabriel · 1 citation
#37A25 #37A50 #37F80 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.01178

Abstract

For Hénon maps, Bianchi and Dinh recently proved the exponential mixing of all orders for the measure of maximal entropy and, as a consequence of the recent work of Björklund and Gorodnik, the CLT for Hölder observables. We extend their results to generic birational maps of ℙ^k. Because of the indeterminacy set, Hölder maps are not stable under iteration, so we need to work with a suitable space of test functions.

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• log-Hölder regularity of currents and equidistribution towards Green currents

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