Maslov P-Index Theory for a Symplectic Path with Applications*

Abstract

The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.

Keywords

Hamiltonian system / Symplectic path / Maslov P-index / Non-periodic boundary problem / 58F05 / 58E05 / 34C25 / 58F10

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