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.
|Title of host publication||Nonlinear Functional Analysis and its Applications|
|Editors||S. P. Singh|
|Place of Publication||Dordrecht, Geramny|
|Publication status||Published - 1986|
|Name||NATO ASI Series C|
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.