Accession Number:

AD0713885

Title:

Convex Functions Harmonic Maps, and the Stability of Hamiltonian Systems.

Descriptive Note:

Interim rept.,

Corporate Author:

NAVAL RESEARCH LAB WASHINGTON D C MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1970-09-24

Pagination or Media Count:

11.0

Abstract:

Trajectories of conservative dynamical systems are particular examples of harmonic maps. If Y is the configuration space of a dynamical system, then a trajectory of the system is a harmonic map from the real line into Y. More generally, let X and Y be Riemannian manifolds with X compact. It is shown that the image of any harmonic map f from X to Y cannot be contained in domains which are too small specifically, that the image of any such f cannot be contained on any domain which supports a convex function. From a modification of the proof it is shown that, except in the neighborhoods of certain exceptional points, a trajectory of a dynamical system cannot lie entirely in any such domain. This fact leads to criteria for the growth and instability of dynamical systems. Author

Subject Categories:

  • Celestial Mechanics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE