Abstract
In this paper, it is proved that, for the networks of weakly coupled pendulum equations \t\t\td2xndt2+λn2sinxn=ϵWn(xn−1,xn,xn−1),n∈Z,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\frac{d^{2} x_{n}}{d t^{2}}+\\lambda_{n}^{2} \\sin x_{n}= \\epsilon W_{n}(x_{n-1},x_{n},x_{n-1}),\\quad n \\in\\mathbb {Z}, $$\\end{document} there are many (positive Lebesgue measure) normally hyperbolic invariant tori which are infinite dimensional in both tangent and normal directions.
Highlights
Introduction and main resultIn the last several decades, models of many coupled oscillators have found diverse applications in various fields of science
Among a lot of examples are the collective dynamics of Josephson junctions [1, 2], lasers [3, 4], relativistic magnetrons [5], chemical reactions [6,7,8,9], circadian pacemakers [10, 11], intestinal electrical rhythms [12], a variety of biological processes [13,14,15], etc
The research of these systems has brought outstanding examples of different types of dynamical behavior that can be induced by the attendance of coupling
Summary
Introduction and main resultIn the last several decades, models of (infinitely) many coupled oscillators have found diverse applications in various fields of science. While all of λn are the same, Yuan [49, 50] obtained similar KAM results for infinitely dimensional Hamiltonian system (1.4) of short range.
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