
Accession Number : ADA134431
Title : Morse Type Index Theory for Flows and Periodic Solutions for Hamiltonian Equations.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Conley,Charles ; Zehnder,Eduard
PDF Url : ADA134431
Report Date : Sep 1983
Pagination or Media Count : 92
Abstract : This paper has two aims. First, in an expository style an index theory for flows is presented, which extends the classical Morsetheory for gradient flows on manifolds. Secondly this theory is applied in the study of the forced oscillation problem of time dependent (periodic in time) and asymptotically linear Hamiltonian equations. Using the classical variational principle for periodic solutions of Hamiltonian systems a Morsetheory for periodic solutions of such systems is established. In particular a winding number, similar to the Maslov index of a periodic solution is introduced, which is related to the Morseindex of the corresponding critical point. This added structure is useful in the interpretation of the periodic solutions found. (Author)
Descriptors : *Hamiltonian functions, Variational principles, Flow, Indexes, Theorems, Theory
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE