Resurgence of inner solutions for perturbations of the McMillan map
Abstract. A sequence of \inner equations" attached to certain perturbations of the McMillan map was considered in [5], 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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/13217 |
| Acceso en línea: | https://hdl.handle.net/2117/13217 https://dx.doi.org/10.3934/dcds.2011.31.165 |
| Access Level: | acceso abierto |
| Palabra clave: | Resurgence exponentially small phenomena splitting of separatrices Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::34 Ordinary differential equations::34C Qualitative theory Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory Classificació AMS::34 Ordinary differential equations::34M Differential equations in the complex domain Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Abstract. A sequence of \inner equations" attached to certain perturbations of the McMillan map was considered in [5], 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 [5]. The present work relies on ideas from resur- gence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use Ecalle's alien derivations to measure the discrepancy between di erent Borel-Laplace sums. |
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