Mixing and CLT for Hénon-Sibony maps: plurisubharmonic observables

2024/07/22 by Vergamini, Marco, Wu, Hao
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.15418

Abstract

Let f be a complex Hénon map and μ its unique measure of maximal entropy. We prove that μ is exponentially mixing of all orders for all (not necessarily bounded) plurisubharmonic observables, and that all plurisubharmonic functions satisfy the central limit theorem with respect to μ. Our results hold more generally for every Hénon-Sibony map on ℂ^k.

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