Accession Number : AD0660052

Title :   NEW RESULTS ON PERIODIC SURFACES AND THE AVERAGING PRINCIPLE.

Descriptive Note : Technical rept.,

Corporate Author : CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS

Personal Author(s) : Diliberto,Stephen P.

Report Date : AUG 1967

Pagination or Media Count : 45

Abstract : In his recent work on periodic surfaces Sacker established the existence of an epsilon-family y = S(theta, epsilon) defined for an open interval of the perturbation parameter epsilon not including zero, i.e. for suitable epsilon superscript 0, S is defined for 0 < epsilon < t superscript 0. One result of this paper is to show lim as epsilon approaches 0 of S(theta, epsilon) exists and to calculate it. The tools developed for doing this also allow one to give a complete version of the 'averaging principle' as a device for finding expansions for solutions--provided one uses the author's generalization of the K-B averaging technique. (Author)

Descriptors :   (*TOPOLOGY, PERIODIC VARIATIONS), (*PERTURBATION THEORY, PERIODIC VARIATIONS), DIFFERENTIAL EQUATIONS, OSCILLATION, HYSTERESIS, VIBRATION, ORBITS, PARTIAL DIFFERENTIAL EQUATIONS, APPROXIMATION(MATHEMATICS), TRANSFORMATIONS(MATHEMATICS), VECTOR SPACES, EXPONENTIAL FUNCTIONS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE