Dichotomy and integral manifolds part II: proof of the continuation principle

Summary

This paper is intended to fill a gap in the preceding part I ( Vol. 14 of this journal, pp. 93–124). The missing proof of Theorem 5.1 is provided in the subsequent Section 8. Thereby a new and effective method for constructing invariant manifolds in the large is demonstrated, namely analytic continuation. The presentation is (almost) self-contained and complete in the sense that considerable technical difficulties which arise from an extensive usage of the implicit function theorem are elaborated. Section 7 is a collection of material from the literature which is reformulated in such a way that it serves our purposes best. Lemma 7.1 is actually taken from [5], the proof is repeated here.

Note that the enumeration (of sections, formulas) which was started in part I is simply carried further. In interpreting quotations part I and II should be regarded as a unit. For the reader’s convenience Section 7 is preceded by a repetition of material from part I. At the end of the paper a selection of earlier references — some have been updated — is added.