Digitale Medien
Springer
Journal of dynamics and differential equations
12 (2000), S. 449-510
ISSN:
1572-9222
Schlagwort(e):
homoclinic orbits
;
center manifolds
;
Shilnikov bifurcation
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract In this article, center-manifold theory is developed for homoclinic solutions of ordinary differential equations or semilinear parabolic equations. A center manifold along a homoclinic solution is a locally invariant manifold containing all solutions which stay close to the homoclinic orbit in phase space for all times. Therefore, as usual, the low-dimensional center manifold contains the interesting recurrent dynamics near the homoclinic orbit, and a considerable reduction of dimension is achieved. The manifold is of class C 1, β for some β〉0. As an application, results of Shilnikov about the occurrence of complicated dynamics near homoclinic solutions approaching saddle-foci equilibria are generalized to semilinear parabolic equations.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1026412926537
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