Multiple brake orbits on convex hypersurfaces under asymmetric pinch conditions

In this paper, we give an example of an asymmetric convex compact hypersurface possessing precisely n brake orbits. For H∈C1(R2n,R) satisfying H(-p,q)=H(p,q) for all (p,q)∈Rn×Rn, we prove multiplicity result of the brake orbits on H-1(1) pinched by not necessarily symmetric hypersurfaces.