6 problems

Berger's high-emergence conjecture. In many spaces of dynamical systems, high emergence is locally typical, in many senses.

Let high emergence mean that the number of probability measures needed to describe a dynamical system up to precision $\varepsilon$ grows super-polynomially in $\varepsilon^{-1}$.…

Let $f$ be a dynamical system with emergence function $\mathcal E_f(\epsilon)$. When … the system is said to have super-polynomial emergence. Super-polynomial emergence conjecture.…

High-emergence conjecture. Dynamics of high emergence are typical in many senses and contexts. This is stated as the first aim of the authors' program on emergence; the source leav…

Maximal-exponent pointwise emergence conjecture. There exists a dense subset $\mathcal D$ of any Newhouse open set of $\mathrm{Diff}^r(M)$ such that, for each $f\in\mathcal D$, one…

Let $M$ be the compact manifold under consideration, and let $\operatorname{Diff}(M)$ denote its diffeomorphism space. Sup-polynomial emergence conjecture. There exists an open set…