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Resurgence of inner solutions for perturbations of the McMillan map

Author
Martin, P.; Sauzin, D.; Martinez-seara, M.
Type of activity
Journal article
Journal
Discrete and continuous dynamical systems. Series A
Date of publication
2011-09
Volume
31
Number
1
First page
165
Last page
207
DOI
https://doi.org/10.3934/dcds.2011.31.165 Open in new window
Repository
http://hdl.handle.net/2117/13217 Open in new window
URL
http://www.aimsciences.org/journals/home.jsp?journalID=1 Open in new window
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...
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.
Keywords
Resurgence, exponentially small phenomena, splitting of separatrices
Group of research
SD - UPC Dynamical Systems

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