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On the reducibility of a class of linear differential equations with quasiperiodic coefficients

Part of: General theory in ordinary differential equations

Published online by Cambridge University Press:  26 February 2010

Xu Junxiang
Xu Junxiang
Affiliation:
Department of Applied Mathematics, Southeast University. Nanjing 210018, P.R. China.
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Abstract

This paper treats the reducibility of the quasiperiodic linear differential equations

where A is a constant matrix with multiple eigenvalues, Q(t) is a quasiperiodic matrix with respect to time t, and ε is a small perturbation parameter. Under some non-resonant conditions, rapidly convergent methods prove that, for most sufficiently small ε, the differential equations are reducible to a constant coefficient differential equation by means of a quasiperiodic change of variables with the same frequencies as Q(t).

MSC classification

Secondary: 34A30: Linear equations and systems, general

Information

Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 443 - 451
Copyright
Copyright © University College London 1999

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References

1. Bogoljubov, N. N., Mitropoliski, J. A. and Samoilenko, A. M.. Methods of Accelerated Convergence in Nonlinear Mechanics (Springer-Verlag, New York, 1976).CrossRefGoogle Scholar
2. Palmer, K.. On the reducibility of the almost periodic systems of linear differential equations. J. Differential Equations, 36 (1980), 374–390.CrossRefGoogle Scholar
3. Johnson, R. A. and Sell, G. R.. Smoothness of spectral subbundles and reducibility of quasiperiodic linear differential systenms. J. Differential Equations, 41 (1981), 262–288.CrossRefGoogle Scholar
4. Jorba, A. and Simo, C.. On the reducibility of linear differential equations with quasiperiodic coefficients. J. Differential Equations, 98 (1992), 111–124.CrossRefGoogle Scholar
5. Arnold, V. I.. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys Z, 18 (1963), 85–191.CrossRefGoogle Scholar
6. Poschel, J.. On elliptic lower dimensional tori in Hamiltonian systems. Math. Z., 202 (1989), 559–608.CrossRefGoogle Scholar
7. Jorba, A., Ramirez-Ros, R. and Villanueva, J.. Effective reducibility of quasiperiodic linear equations close to constant coefficients. Preprint, Dept. de Matematica Aplicada I, ETSE1B, Universitat Politecnica de Catalunya (1995).Google Scholar