Resurgence of inner solutions for perturbations of the McMillan map

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/13217

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author	Martín, Pau
dc.contributor.author	Sauzin, D.
dc.contributor.author	Martínez-Seara Alonso, M. Teresa
dc.date	2011-09
dc.identifier.citation	Martín, P.; Sauzin, D.; Martínez-Seara, M. Resurgence of inner solutions for perturbations of the McMillan map. "Discrete and continuous dynamical systems. Series A", Setembre 2011, vol. 31, núm. 1, p. 165-207.
dc.identifier.citation	1078-0947
dc.identifier.citation	10.3934/dcds.2011.31.165
dc.identifier.uri	http://hdl.handle.net/2117/13217
dc.language.iso	eng
dc.relation	http://www.aimsciences.org/journals/home.jsp?journalID=1
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Resurgence
dc.subject	exponentially small phenomena
dc.subject	splitting of separatrices
dc.subject	Sistemes dinàmics diferenciables
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject	Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject	Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory
dc.subject	Classificació AMS::34 Ordinary differential equations::34M Differential equations in the complex domain
dc.title	Resurgence of inner solutions for perturbations of the McMillan map
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	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.
dc.description.abstract	Peer Reviewed

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