Attraction

Abstract

Averaging procedures for initial value problems, and their basic error estimates, have been established in the last two chapters under various circumstances. Usually the error estimates are valid for a time of order 1/ε, although occasionally this can be extended to 1/ε^j+1 for some integer j > 1 (see Theorem 2.9.4). In this chapter and the next, we investigate circumstances under which the validity of averaging can be extended still farther. Results can sometimes be obtained for all t ≥ 0, or for all t such that the solution remains in a certain region. This chapter is concerned with solutions that approach a particular solution that is an attractor.