Wayne, C. Eugene2007-08-162007-08-161983https://hdl.handle.net/11299/4722The proof of the results on the KAM theory of systems with short range interactions, stated in [4] is completed. Estimates on the decay of the interactions generated by the iterative procedure in the KAM theorem are proved, as well as the modification of the theorems of [1-3] needed for our results.