Abstract
The proof of the results on the KAM theory of systems with short range interactions, stated in [6] 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 [2–3] needed for results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brydges, D., Fröhlich, J., and Spencer, T.: The random walk representation of classical spin systems and correlation inequalities. Commun. Math. Phys.83, 123 (1982)
Chierchia, L., Gallavotti, G.: Smooth prime integrals for quasi-integrable Hamiltonian systems. I1 Nuovo Cimento67B, 277 (1982)
Gallavotti, G.: ‘Perturbation theory for classical Hamiltonian systems.’ In: Scaling and Self-Similarity in Physics, Fröhlich, J. (ed.). Boston, MA: Birkhäuser Boston, Inc., 1983
Pöschel, J.: Commun. Pure Appl. Math.35, 653 (1982)
Symmanzik, K.: Euclidean quantum field theory. In: Local Quantum Theory Jost, (ed.), New York, London: Academic Press, 1969
Wayne, C. E.: The KAM Theory of Systems with Short Range Interactions, I. Institute for Mathematics and its Applications, Preprint Series No. 32 (1983). Commun. Math. Phys. 1984
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
This work was completed while the author was at the Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN, 55455, USA
Supported in part by NSF Grant DMS-8403664
Rights and permissions
About this article
Cite this article
Wayne, C.E. The KAM theory of systems with short range interactions, II. Commun.Math. Phys. 96, 331–344 (1984). https://doi.org/10.1007/BF01214578
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01214578