Exponentially Small Splitting of Invariant Manifolds of Parabolic Points.

Intro -- Contents -- Introduction -- 1. Notation and main results -- 1.1. Notation and hypotheses -- 1.2. Main results -- 1.3. Example -- 2. Analytic properties of the homoclinic orbit of the unperturbed system -- 2.1. Introduction and main results -- 2.2. Proof of Proposition 2.1 -- 3. Parameterization of local invariant manifolds -- 3.1. Introduction -- 3.2. Definitions and main result -- 3.3. Averaging of the equation -- 3.4. Estimates for the Poincaré map -- 3.5. The operators B and B -- 3.6. Proof of Theorem 3.1 -- 4. Flow box coordinates -- 4.1. Introduction -- 4.2. Definitions and main result -- 4.3. A preliminary change of variables -- 4.4. The unperturbed case -- 4.5. Flow box coordinates in a complex domain -- 4.6. Proof of Theorem 4.2 -- 5. The Extension Theorem -- 6. Splitting of separatrices -- 6.1. Introduction -- 6.2. The splitting function -- 6.3. Proof of Theorem 1.1 and its corollary -- 6.4. Proof of Lemma 6.4 -- 6.5. Proof of Corollary 1.1 -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.