6 problems

Polynomial growth conjecture. There exist $N\in\mathbb{N}$ and $T,C>0$ such that

Consider the diffusive Lotka–Volterra strongly competitive system on an interval $(0,L)$ with boundary-constrained controls, parameters $a>0$ and $b>1$ satisfying $b>a$, initial da…

Controllability-diameter conjecture. For every such Hamiltonian, the implication

Let $\Omega$ be the rectangular domain described above, and let $L^2_{\operatorname{div}}(\Omega)$ denote the space of square-integrable divergence-free vector fields tangent to…

Let $G(n,1/2)$ be the Erdős–Rényi random graph on $n$ vertices, and let $G$ be controllable and minimally controllable when it has the corresponding controllability properties for…

Finite-jet conjecture. There exists $N\in\mathbb{N}$ such that every such system $\mathcal{Y}$ is small-time locally controllable from $x_0$. The conjecture asks whether small-time…