  By coupling a Hamiltonian mechanical system with a linear Hamiltonian field
theory one obtains an infinite-dimensional Hamiltonian system with regularizing
nonlinearity, where the underlying phase space is given by the product of a
finite-dimensional symplectic manifold with an infinite-dimensional linear
symplectic Hilbert space. After our compactness results we continue our program
for defining a Floer homology theory for this class of infinite-dimensional
Hamiltonian systems. Based on the presence of small divisors we introduce a new
notion of nondegeneracy for time-periodic solutions which allows us to prove
that the linearization of the nonlinear Floer operator is Fredholm when viewed
as a map between suitable Sobolev space completions.
