Abstract
The existence of quasiperiodic trajectories for Hamiltonian systems consisting of long chains of nearly identical subsystems, with interactions which decay rapidly with increasing distance between the interacting components, is studied. Such models are of interest in statistical mechanics. It is shown that nonergodic motions persist for much larger perturbations than prior work indicated. If the number of degrees of freedom of the system isN, the allowed perturbation decreases only as an inverse power ofN, as the number of degrees of freedom increases, rather than the inverse power ofN! which previous estimates yielded.
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Communicated by A. Jaffe
This work was completed while the author was at the Institute for Mathematics and Its Applictations, University of Minnesota, Minneapolis, MN, 55455, USA
Supported in part by NSF Grant DMS-8403664
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Wayne, C.E. The KAM theory of systems with short range interactions, I. Commun.Math. Phys. 96, 311–329 (1984). https://doi.org/10.1007/BF01214577
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DOI: https://doi.org/10.1007/BF01214577