Hyperbolic Closed Characteristics on Compact Convex Smooth Hypersurfaces inR2n

In this paper we prove that on every compactC2hypersurface inR2nbounding a convex set with non-empty interior, either there exists a sequence of variationally visible hyperbolic closed characteristcs with their minimal periods tending to infinity, or there exists at least one variationally visible nonhyperbolic closed characteristic