  In this paper we prove the existence of real-analytic natural Hamiltonian
systems - i.e. where H(q,p)=T(q,p)+V(q) in the 2N-dimensional real space, where
N is any integer greater than 1 - with non critical energy levels E for the
potential V such that the sublevel E of V is homeomorphic to the N-dimensional
disk, and that only one brake orbit of energy E exists. A famous conjecture
formulated by H. Seifert in 1948 claimed the existence of at least N distinct
brake orbits for this situation.
