Morse Type Index Theory for Flows and Periodic Solutions for Hamiltonian Equations.

Abstract

This paper has two aims. First, in an expository style an index theory for flows is presented, which extends the classical Morse-theory 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 Morse-theory 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 Morse-index of the corresponding critical point. This added structure is useful in the interpretation of the periodic solutions found. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1983
Accession Number
ADA134431

Entities

People

  • Charles Conley
  • Eduard Zehnder

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Algebraic Topology
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Euler Equations
  • Integral Equations
  • Linear Systems
  • Mathematics
  • Notation
  • Partial Differential Equations
  • Point Theorem
  • Topology
  • United States
  • Variational Principles

Fields of Study

  • Mathematics

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