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Título: | Resurgence of inner solutions for perturbations of the McMillan map |
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Autor/a: | Martínez-Seara Alonso, M. Teresa; Sauzin, D.; Martín de la Torre, Pablo |
Otros autores: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
Abstract: | A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums. |
Materia(s): | -Àrees temàtiques de la UPC::Matemàtiques i estadística -Pertorbació (Matemàtica) -Equacions diferencials |
Derechos: | Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Tipo de documento: | Artículo - Borrador Informe |
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