Accession Number : AD0712706

Title :   ON A THEOREM OF K. T. CHEN,

Corporate Author : BROWN UNIV PROVIDENCE R I

Personal Author(s) : Braun,Martin

Report Date : 13 AUG 1970

Pagination or Media Count : 16

Abstract : The report describes mappings M of the real line into itself of the form M: x sub 1 = x + hx sup nu + f(x). Recently, K. T. Chen proved, via the Schauder Fixed Point Theorem, that M possessed the normal form x sub 1 = x + hx + c(x sup (2nu - 1)). Here the Contracting Mapping Principle is used to prove that M has the normal form x sub 1 = x + hx sup nu thus eliminating the extraneous term c(x sup (2nu - 1)). The main idea is to derive sharp estimates on how fast the iterates of a point enter or leave the origin. It is to be noted that the methods developed here can be generalized to prove the existence of invariant manifolds for differential equations whose linear part has one eigenvalue zero. (Author)

Descriptors :   (*MAPPING(TRANSFORMATIONS), THEOREMS), (*DIFFERENTIAL EQUATIONS, TOPOLOGY), ITERATIONS, INVARIANCE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE