Accession Number : AD0622528

Title :   MORSE THEORY AND LIAPUNOV FUNCTIONS,

Corporate Author : WESTERN RESERVE UNIV CLEVELAND OHIO

Personal Author(s) : Leighton,Walter

Report Date : JUN 1964

Pagination or Media Count : 12

Abstract : When an autonomous system of differential equations dx/dt = f(x) (x = x sub i, x sub 2, . . . , x sub n has an isolated equilibrium point at (x) = (0) which is asymptotically stable, it is of interest to determine a region of attraction containing the equilibrium point; that is, a region R with the property that every half-trajectory which has a point in R when t = t sub 0 tends to the equilibrium point at the origin as t approaches infinity. It is shown how methods due to Morse can be used with great effectiveness in the determination of such regions of attraction. A new condition for global asymptotic stability of the equilibrium point then emerges in a natural fashion.

Descriptors :   (*TRAJECTORIES, CALCULUS OF VARIATIONS), (*DIFFERENTIAL EQUATIONS, TRAJECTORIES), FUNCTIONAL ANALYSIS, STABILITY, FUNCTIONS(MATHEMATICS), SET THEORY, INTEGRALS

Distribution Statement : APPROVED FOR PUBLIC RELEASE