8 problems

Let $W\subset{\mathbb R}^{2n}$ be a star-shaped domain, and consider the Reeb flow on its boundary $\partial W$. A closed Reeb orbit is prime if it is not an iterate of another clo…

Let $\Sigma^{2n-1}$ bound a strictly convex domain in $\mathbb{R}^{2n}$. Elliptic orbit conjecture. There exists at least one elliptic closed Reeb orbit on $\Sigma$. The source des…

Let $\Sigma^{2n-1}$ bound a convex domain in $\mathbb{R}^{2n}$, with $n\geq 2$, and let $\mathcal{T}(\Sigma)$ denote the set of prime closed Reeb orbits on $\Sigma$. A closed Reeb…

Let $\Sigma^{2n-1}$ bound a star-shaped domain in $\mathbb{R}^{2n}$. Higher-dimensional two-or-infinity conjecture. For each such $\Sigma$, … The dimension-four case is solved by t…

Let $\Sigma^{2n-1}$ be the boundary of a star-shaped domain in $\mathbb{R}^{2n}$, and let $\mathcal{T}(\Sigma)$ denote the set of prime closed Reeb orbits on $\Sigma$. Multiplicity…

Let $M$ be the smooth boundary of a star-shaped domain in ${\mathbb R}^{2n}$. A Reeb pseudo-rotation is a Reeb flow on $M$ with finitely many prime closed orbits. HZ-conjecture. Th…

Let $(S^{2n+1},\xi_{std})$ be the standard contact sphere, and let $\alpha$ be any contact form on it. A closed orbit is simple if it is not an iterate of another closed orbit. Clo…

Consider the two-dimensional Tremblay–Turbiner–Winternitz Hamiltonian … with $0\leqslant\theta\leqslant\frac{\pi}{2k}$, $0\leqslant r<\infty$, angular frequency $\omega$, nonnegati…