RESULTS ON INVARIANT WHISKERED TORI FOR FIBERED HOLOMORPHIC MAPS AND ON COMPENSATED DOMAINS.

RESULTS ON INVARIANT WHISKERED TORI FOR FIBERED HOLOMORPHIC MAPS AND ON COMPENSATED DOMAINS.

ABSTRACT

This thesis is composed of two independent papers: Construction of whiskered invariant tori for fibered holomorphic maps In this paper we present a very general theory that includes results on the persistence of quasi-periodic orbits of systems subject to quasi-periodic perturbations. Such quasi-periodic systems appear naturally in many applications where systems are subject to external perturbations of quasi-periodic nature. This is joint work with Rafael de la Llave. The paper takes up Chapters I - VII of the thesis. We give a brief motivation in Chapter I. In Chapter II we introduce informally the spaces of analytic functions and some number-theoretic and non-degeneracy conditions which are rigorously defined in Chapter III. In Chapter IV we present the Main result of the paper, and present the pseudocode for an Algorithm (Algorithm 1) which efficiently computes the invariant objects that have been introduced in Chapter II. A brief review of the most important references in the literature which are related with our work is in Section 4.5. The proof of the main result, theorem 1, takes up Chapters V-VII. We present an outline for the proof of theorem 1 in Section 4.3.

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