The Iteration Formulae of the Maslov-Type Index Theory in Weak Symplectic Hilbert Space

Citation:

Li WU,Chaofeng ZHU.The Iteration Formulae of the Maslov-Type Index Theory in Weak Symplectic Hilbert Space[J].Chinese Annals of Mathematics B,2018,39(1):17~32
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Authors:

Li WU; Chaofeng ZHU

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11221091, 11471169) and the Key Laboratory of Pure Mathematics and Combinatorics, the Ministry of Education of China.
Abstract: The authors prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space. Then a direct proof of the iteration formulae for the Maslov-type indices of symplectic paths is given.

Keywords:

Maslov-type index, Positive path, Iteration formula

Classification:

53D12, 58J30
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