title: Multidimensional Hamiltonian chaos.
abstract: In this review the description of nontrivial hyperbolic sets of Hamiltonian systems having singular points (a saddle, a saddle-focus) with homoclinic orbits is given. On the basis of Melnikov's method the criteria for the existence of homoclinic orbits to the singular points in systems close to integrable ones are pointed out.
authors.affiliation: Research Institute for Applied Mathematics and Cybernetics, Nizhnii Novgorod, USSR.
authors.forename: L. P.
authors.initials: LP
authors.lastname: Shilnikov