The Morse index of an isolated invariant set is a connected simple system
نویسندگان
چکیده
منابع مشابه
Connected Simple Systems and the Conley Index of Isolated Invariant Sets
The object of this paper is to present new and simplified proofs for most of the basic results in the index theory for flows. Simple, explicit formulae are derived for the maps which play a central role in the theory. The presentation is self-contained.
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15 صفحه اولWhen the Morse index is infinite
Let f be a smooth Morse function on an infinite dimensional separable Hilbert manifold, all of whose critical points have infinite Morse index and co-index. For any critical point x choose an integer a(x) arbitrarily. Then there exists a Riemannian structure on M such that the corresponding gradient flow of f has the following property: for any pair of critical points x, y, the unstable manifol...
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15 صفحه اولA generalized Morse index theorem
In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1981
ISSN: 0022-0396
DOI: 10.1016/0022-0396(81)90028-0