Multiple brake orbits on convex hypersurfaces under asymmetric pinch conditions Original Research Article

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