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- W2004193600 abstract "Let f be an holomorphic endomorphism of $${mathbb{P}^k}$$ and μ be its measure of maximal entropy. We prove an almost sure invariance principle for the systems $${(mathbb{P}^k,f,mu)}$$ . Our class $${mathcal {U}}$$ of observables includes the Hölder functions and unbounded ones which present analytic singularities. The proof is based on a geometric construction of a Bernoulli coding map $${omega: (Sigma, s, nu) to (mathbb{P}^k,f,mu)}$$ . We obtain the invariance principle for an observable ψ on $${(mathbb{P}^k,f,mu)}$$ by applying Philipp–Stout’s theorem for $${chi = psi circ omega}$$ on (Σ, s, ν). The invariance principle implies the central limit theorem as well as several statistical properties for the class $${mathcal {U}}$$ . As an application, we give a direct proof of the absolute continuity of the measure μ when it satisfies Pesin’s formula. This approach relies on the central limit theorem for the unbounded observable log $${{tt Jac}, f in mathcal{U}}$$ ." @default.
- W2004193600 created "2016-06-24" @default.
- W2004193600 creator A5078980402 @default.
- W2004193600 date "2008-12-16" @default.
- W2004193600 modified "2023-09-30" @default.
- W2004193600 title "Bernoulli coding map and almost sure invariance principle for endomorphisms of $${mathbb P^k}$$" @default.
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- W2004193600 doi "https://doi.org/10.1007/s00440-008-0192-4" @default.
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