  We survey the basic notions of scattering theory in Hamiltonian mechanics
with a particular attention to the analogies with scattering theory in quantum
mechanics. We discuss the scattering symplectomorphism, which is analogous to
the scattering matrix. We prove identities which relate the Calabi invariant of
the scattering symplectomorphism to the total time delay and the regularised
phase space volume. These identities are analogous to the Birman-Krein formula
and the Eisenbud-Wigner formula in quantum scattering theory.
