  We construct on $\R^{2d}$, for any $d \geq 3$, smooth Hamiltonians having an
elliptic equilibrium with an arbitrary frequency, that is not accumulated by a
positive measure set of invariant tori. For $d\geq 4$, the Hamiltonians we
construct have not any invariant torus of dimension $d$. Our examples are
obtained by a version of the successive conjugation scheme {\it \`a la}
Anosov-Katok.
