Schroer–Sauer–Ott–Yorke predictability conjecture

Let $T\colon X \to X$ be a smooth diffeomorphism of a compact Riemannian manifold $X$ with a natural measure $\mu$ of information dimension $\operatorname{ID}(\mu)=D$. An observable $h\colon X\to\mathbb R$ is called almost surely $k$-predictable with respect to $\mu$ when its $k$-delay prediction error vanishes for $\mu$-almost every state. SSOY predictability conjecture. For a generic observable $h\colon X\to\mathbb R$, $h$ is almost surely $k$-predictable with respect to $\mu$ for $k>D$. This conjecture concerns the number of time-delayed scalar measurements needed to predict future observations of a chaotic system; the paper states that its general version is proved for Lipschitz systems and prevalent Lipschitz observables, while the original smooth natural-measure formulation is thereby recovered in the stated setting.