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) : Gordon,William B.

Report Date : 24 SEP 1970

Pagination or Media Count : 11

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)

Descriptors :   (*ALGEBRAIC TOPOLOGY, THEOREMS), (*N-BODY PROBLEM, HAMILTONIAN), CELESTIAL MECHANICS, CONVEX SETS, POTENTIAL THEORY, GEODESICS, STABILITY

Subject Categories : Celestial Mechanics
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE