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Mixing and CLT for H\'enon-Sibony maps: plurisubharmonic observables

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arxiv 2407.15418 v3 pith:2YQOMY2F submitted 2024-07-22 math.CV math.DS

Marco Vergamini , Hao Wu This is my paper · ORCID
classification math.CVmath.DS
keywords plurisubharmonicenon-sibonymixingobservablesboundedcentralcomplexenon
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abstract

Let $f$ be a complex H\'enon map and $\mu$ its unique measure of maximal entropy. We prove that $\mu$ 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 $\mu$. Our results hold more generally for every H\'enon-Sibony map on $\mathbb{C}^k$.

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  1. Exponential mixing of all orders on K\"ahler manifolds: (quasi-)plurisubharmonic observables

    math.CV 2025-05 conditional novelty 6.0 of 10

    For compact Kähler automorphisms with simple cohomology action, the maximal-entropy measure is exponentially mixing of all orders for all d.s.h. observables, with the central limit theorem as a consequence.

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