  A method to construct integrable deformations of Hamiltonian systems of ODEs
endowed with Lie-Poisson symmetries is proposed by considering Poisson-Lie
groups as deformations of Lie-Poisson (co)algebras. Moreover, the underlying
Lie-Poisson symmetry of the initial system of ODEs is used to construct
integrable coupled systems, whose integrable deformations can be obtained
through the construction of the appropriate Poisson-Lie groups that deform the
initial symmetry. The approach is applied in order to construct integrable
deformations of both uncoupled and coupled versions of certain integrable types
of R\"ossler and Lorenz systems. It is worth stressing that such deformations
are of non-polynomial type since they are obtained through an exponentiation
process that gives rise to the Poisson-Lie group from its infinitesimal Lie
bialgebra structure. The full deformation procedure is essentially algorithmic
and can be computerized to a large extent.
