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On the reducibility of linear differential equations with quasiperiodic coefficients which are degenerate
Author(s):
Xu
Junxiang;
Zheng
Qin
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1445-1451.
MSC (1991):
Primary 34D20;
Secondary 34C05
MathSciNet review:
1458272
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Abstract:
This paper proves the reducibility of a class of linear differential equations with quasiperiodic coefficients which are degenerate with respect to a small perturbation parameter. Our results generalize some that were obtained by Jorba and Simó.
References:
- [1]
- N. N. Bogoljubov, J. A. Mitropoliski and A. M. Samoilenko, Methods of Accelerated Convergence in Nonlinear Mechanics, Springer-Veriage, New York (1976). MR 53:1156
- [2]
- Angel Jorba and Carles Simó, On the Reducibility of Linear Differential Equations with Quasiperiodic Coefficients, J. Diff. Equa. 98 (1992), 111-124. MR 94f:34024
- [3]
- V. I. Arnold, Small denominators and problems of stability of motion in classical and celestial mechanics, Russian Math. Surveys 18 (1963), no. 6, 85-191. MR 30:943
- [4]
- Pöschel, J., On elliptic lower dimensional tori in Hamiltonian systems, Math. Z. 202 (1989), 559-608. MR 91a:58065
- [5]
- Whitney, H., Analytical extensions of differentiable functions defined in closed sets, Trans. A.M.S. 36 (1934), 63-89.
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Additional Information:
Xu
Junxiang
Affiliation:
Department of Mathematics and Mechanics, Southeast University, Nanjing 210096, People's Republic of China
Email:
xujun@seu.edu.cn
Zheng
Qin
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China
DOI:
10.1090/S0002-9939-98-04523-7
PII:
S 0002-9939(98)04523-7
Keywords:
Linear differential equations,
reducibility,
quasiperiodic,
KAM iteration
Received by editor(s):
October 22, 1996
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1998,
American Mathematical Society
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