Accession Number:

AD0712706

Title:

ON A THEOREM OF K. T. CHEN,

Descriptive Note:

Corporate Author:

BROWN UNIV PROVIDENCE R I

Personal Author(s):

Report Date:

1970-08-13

Pagination or Media Count:

16.0

Abstract:

The report describes mappings M of the real line into itself of the form M x sub 1 x hx sup nu fx. Recently, K. T. Chen proved, via the Schauder Fixed Point Theorem, that M possessed the normal form x sub 1 x hx cx 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 cx 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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE