  Regular perturbative Lagrangians that admit approximate Noether symmetries
and approximate conservation laws are studied. Specifically, we investigate the
connection between approximate Noether symmetries and collineations of the
underlying manifold. In particular we determine the generic Noether symmetry
conditions for the approximate point symmetries and we find that for a class of
perturbed Lagrangians, Noether symmetries are related to the elements of the
Homothetic algebra of the metric which is defined by the unperturbed
Lagrangian. Moreover, we discuss how exact symmetries become approximate
symmetries. Finally, some applications are presented.
