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Finite-order exponential mixing does not imply the central limit theorem
We show that finite-order exponential mixing does not imply the central limit theorem for smooth diffeomorphisms. For every integer $R\geq2$, we construct a $\mathcal{C}^{\infty}$ diffeomorphism $T:M\to M$ of a compact smooth manifold $M$ and a $T$-invariant probability measure $μ$ such that $(T,μ)$
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