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We discuss the final stages of double ionization of atoms in a stronglinearly polarized laser field within a classical model. We propose that alltrajectories leading to non-sequential double ionization pass close to a saddlein phase space which we identify and characterize. The saddle lies in a twodegree of freedom subspace of symmetrically escaping electrons. Thedistribution of longitudinal momenta of ions as calculated within the subspaceshows the double hump structure observed in experiments. Including a symmetricbending mode of the electrons allows us to reproduce the transverse ionmomenta. We discuss also a path to sequential ionization and show that it doesnot lead to the observed momentum distributions.Comment: 10 pages, 10 figures; fig.6 and 7 exchanged in the final version  accepted for publication in Phys. Rev.

Pathways to double ionization of atoms in strong fields