Typicality of super-polynomial emergence in dynamical systems

Let $f$ be a dynamical system with emergence function $\mathcal E_f(\epsilon)$. When

$$\limsup_{\epsilon \to 0} \frac{\log \mathcal E_f(\epsilon)}{- \log \epsilon }=\infty,$$

the system is said to have super-polynomial emergence. Super-polynomial emergence conjecture. Super polynomial emergence is typical in many senses and in many categories of dynamical systems. This conjecture concerns the prevalence of systems whose global statistical behavior is more complex than polynomial emergence; the source does not specify a single meaning of typicality or provide a general resolution.