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Mixing and CLT for H\'enon-Sibony maps: plurisubharmonic observables
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Mixing and CLT for H\'enon-Sibony maps: plurisubharmonic observables
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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Cited by 1 Pith paper
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On the support of measures of large entropy for H\'enon-Sibony maps
Every ergodic f-invariant measure with entropy > log max{d_+^{p-1}, d_-^{k-p-1}} is supported on the Julia set J.
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