Asymptotic decomposition of slow integral manifolds

1994 ◽  
Vol 35 (6) ◽  
pp. 1119-1132 ◽  
Author(s):  
L. I. Kononenko ◽  
V. A. Sobolev
Keyword(s):  
Asymptotic Decomposition ◽  
Integral Manifolds

Integral manifolds of differential equations with rapidly rotating phase

1969 ◽  
Vol 12 (11) ◽  
pp. 1243-1252 ◽  
Author(s):  
A. S. Gurtovnik ◽  
Yu. I. Neimark
Keyword(s):  
Differential Equations ◽  
Integral Manifolds

Averaging and integral manifolds

1970 ◽  
Vol 2 (2) ◽  
pp. 197-222 ◽  
Author(s):  
W. A. Coppel ◽  
K. J. Palmer
Keyword(s):  
Autonomous System ◽  
Method Of Characteristics ◽  
Integral Manifold ◽  
Artificial Viscosity ◽  
Original Method ◽  
Method Of Averaging ◽  
System Of Differential Equations ◽  
Viscosity Term ◽  
Integral Manifolds ◽  
The Individual

An integral manifold for a system of differential equations is a manifold such that any solution of the equations which has a point on it is entirely contained on it. The method of averaging establishes the existence of such a manifold for a system which is a perturbation of an autonomous system with a periodic orbit. The existence of the manifold is established here under more general hypotheses, namely for perturbations which are ‘integrally small’. The method differs from the original method of Bogolyubov and Mitropolskii and operates directly with the individual solutions. This is made possibly by the use of an appropriate norm, and is equivalent to solving the partial differential equation which occurs in work by Moser and Sacker by the method of characteristics rather than by the introduction of an artificial viscosity term. Moreover, detailed smoothness properties of the manifold are obtained. For periodic perturbations the integral manifold is a torus and these smoothness properties are just sufficient to permit the application of Denjoy's theorem.

scholarly journals Generic integral manifolds for weight two period domains

2004 ◽  
Vol 356 (6) ◽  
pp. 2241-2249
Author(s):  
James A. Carlson ◽  
Domingo Toledo
Keyword(s):  
Integral Manifolds
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