Abstract
We prove that there exists an open set of irreducible systems in the space of systems of linear differential equations with quasiperiodic skew-adjoint matrices and fixed frequency module.
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REFERENCES
L. H. Eliasson, “Reducibility and point spectrum for linear quasiperiodic skew-products,” in: Proceedings of the International Congress of Mathematicians, Vol. II. Invited Lectures, Berlin (1998), pp. 779–787.
L. H. Eliasson, Ergodic Skew Systems on \({\mathbb{T}}^d \times SO\left( {{3,\mathbb{R}}} \right)\), Preprint, ETH-Zürich, Zürich (1991).
R. Krikorian, “Réducibilité presque partout des systèmes quasi-périodiques dans le cas SO(3, R),” C. R. Acad. Sci. Paris. Série I, 321, 1039–1044 (1995).
V. I. Tkachenko, “On linear systems with quasiperiodic coefficients and bounded solutions,” Ukr. Mat. Zh., 48, No. 10, 1410–1417 (1996).
K. J. Palmer, “On the reducibility of almost periodic systems of linear differential equations,” J. Different. Equat., 36, No. 2, 374–390 (1980).
M. G. Nerurkar and H. J. Sussmann, “Construction of minimal cocycles arising from specific differential equations,” Isr. J. Math., 100, 309–326 (1997).
M. G. Lyubarskii, “On one generalization of the Floquet – Lyapunov theorem,” Dokl. Akad. Nauk SSSR, 213, No. 4, 780–782 (1973).
V. I. Tkachenko, “On uniformly stable linear quasiperiodic systems,” Ukr. Mat. Zh., 49, No. 7, 1102–1108 (1997).
V. I. Tkachenko, “On linear almost periodic systems with bounded solutions,” Bull. Austral. Math. Soc., 55, No. 2, 177–184 (1997).
Y. Pomeau, B. Dorizzi, and B. Grammaticos, “Chaotic Rabi oscillations under quasiperiodic perturbation,” Phys. Rev. Lett., 56, 681–684 (1986).
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Tkachenko, V.I. On Reducibility of Systems of Linear Differential Equations with Quasiperiodic Skew-Adjoint Matrices. Ukrainian Mathematical Journal 54, 519–526 (2002). https://doi.org/10.1023/A:1020581920832
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DOI: https://doi.org/10.1023/A:1020581920832