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MORSE-THEORY FOR PERIODIC-SOLUTIONS OF HAMILTONIAN-SYSTEMS AND THE MASLOV INDEX
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UNSPECIFIED (1992) MORSE-THEORY FOR PERIODIC-SOLUTIONS OF HAMILTONIAN-SYSTEMS AND THE MASLOV INDEX. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 45 (10). pp. 1303-1360. ISSN 0010-3640.
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Abstract
In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chem class of the tangent bundle vanish over pi2(M). The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an index theorem for the Fredholm operator which plays a central role in Floer homology. The index formula involves the Maslov index of nondegenerate contractible periodic solutions. This Maslov index plays the same role as the Morse index of a nondegenerate critical point does in finite dimensional Morse theory. We shall use this connection between Floer homology and Maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every 1-periodic solution has at least one Floquet multiplier which is not equal to 1.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | ||||
Publisher: | JOHN WILEY & SONS INC | ||||
ISSN: | 0010-3640 | ||||
Official Date: | December 1992 | ||||
Dates: |
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Volume: | 45 | ||||
Number: | 10 | ||||
Number of Pages: | 58 | ||||
Page Range: | pp. 1303-1360 | ||||
Publication Status: | Published |
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