An index for Hamiltonian systems with a natural order structure

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Abstract

A brief account is given of degree theoretical considerations which arise when studying Hamiltonian systems whose ‘kinetic energy’ is indefinite with a negative cone of ellipsoidal cross-section in ℝn. Such Hamiltonian systems enjoy a powerful monotonicity property and the purpose of these notes is to explain how this is so, and how it leads to very natural theorems on the existence of homoclinic and periodic orbits.
Original languageEnglish
Title of host publicationNonlinear Functional Analysis and its Applications
EditorsS. P. Singh
Place of PublicationDordrecht, Geramny
PublisherSpringer
Pages147-160
Publication statusPublished - 1986

Publication series

NameNATO ASI Series C
Volume173

Cite this

Toland, J. (1986). An index for Hamiltonian systems with a natural order structure. In S. P. Singh (Ed.), Nonlinear Functional Analysis and its Applications (pp. 147-160). (NATO ASI Series C; Vol. 173). Springer.