2 problems

Let $\Sigma\in\mathcal{H}(2n)$ be a compact convex hypersurface, and let $^{\#}\widetilde{\mathcal{J}}(\Sigma)$ denote the number of geometrically distinct closed characteristics o…

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…