  We use recent results that localized excitations in nonlinear Hamiltonian
lattices can be viewed and described as multiple-frequency excitations. Their
dynamics in phase space takes place on tori of corresponding dimension. For a
one-dimensional Hamiltonian lattice with nearest neighbour interaction we
transform the problem of solving the coupled differential equations of motion
into a certain mapping $M_{l+1}=F(M_l,M_{l-1})$, where $M_l$ for every $l$
(lattice site) is a function defined on an infinite discrete space of the same
dimension as the torus. We consider this mapping in the 'tails' of the
localized excitation, i.e. for $l \rightarrow \pm \infty$. For a generic
Hamiltonian lattice the thus linearized mapping is analyzed. We find conditions
of existence of periodic (one-frequency) localized excitations as well as of
multiple frequency excitations. The symmetries of the solutions are obtained.
As a result we find that the existence of localized excitations can be a
generic property of nonlinear Hamiltonian lattices in contrast to nonlinear
Hamiltonian fields.

Chaotic Dynamics;Chaotic Dynamics