An index for Hamiltonian systems with a natural order structure

John Toland

An index for Hamiltonian systems with a natural order structure

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Other chapter contribution

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 language	English
Title of host publication	Nonlinear Functional Analysis and its Applications
Editors	S. P. Singh
Place of Publication	Dordrecht, Geramny
Publisher	Springer
Pages	147-160
Publication status	Published - 1986

Publication series

Name	NATO ASI Series C
Volume	173

Cite this

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title = "An index for Hamiltonian systems with a natural order structure",

abstract = "A brief account is given of degree theoretical considerations which arise when studying Hamiltonian systems whose {\textquoteleft}kinetic energy{\textquoteright} 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.",

author = "John Toland",

year = "1986",

language = "English",

series = "NATO ASI Series C",

publisher = "Springer",

pages = "147--160",

editor = "Singh, {S. P.}",

booktitle = "Nonlinear Functional Analysis and its Applications",

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T1 - An index for Hamiltonian systems with a natural order structure

AU - Toland, John

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

M3 - Other chapter contribution

T3 - NATO ASI Series C

SP - 147

EP - 160

BT - Nonlinear Functional Analysis and its Applications

A2 - Singh, S. P.

PB - Springer

CY - Dordrecht, Geramny

ER -

An index for Hamiltonian systems with a natural order structure

Abstract

Publication series

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