Seifert Conjecture in the Even Convex Case

In this paper, we prove that there exist at least n geometrically distinct brake orbits on every C² compact convex symmetric hypersurface Σ in ?²ⁿ satisfying the reversible condition NΣ = Σ with N = diag(?I_n,Iⁿ). As a consequence, we show that if the Hamiltonian function is convex and even, then Seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integern. © 2014 Wiley Periodicals, Inc.