Quasi-periodic solutions of nonlinear random Schrödinger equations

Abstract

In this paper, let $\Sigma \subset {\mathbb{R}}^6$ be a compact convex hypersurface. We prove that if $\Sigma$ carries only finitely many geometrically distinct closed characteristics, then at least two of them must possess irrational mean indices. Moreover, if $\Sigma$ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.