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High-precision computations of divergent asymptotic series and homoclinic phenomena
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Gelfreich, Vassili and Simó i Torres, Carles. (2008) High-precision computations of divergent asymptotic series and homoclinic phenomena. Discrete and Continuous Dynamical Systems. Series B, Vol.10 (No.2-3). pp. 511-536. ISSN 1531-3492
Full text not available from this repository.Abstract
We study asymptotic expansions for the exponentially small splitting of separatrices of area preserving maps combining analytical and numerical points of view. Using analytic information, we conjecture the basis of functions of an asymptotic expansion and then extract actual values of the coefficients of the asymptotic series numerically. The computations are performed with high-precision arithmetic, which involves up to several thousands of decimal digits. This approach allows us to obtain information which is usually considered to be out of reach of numerical methods. In particular, we use our results to test that the asymptotic series are Gevrey-1 and to study positions and types of singularities of their Borel transform. Our examples are based on generalisations of the standard and Henon maps.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Asymptotic expansions, Divergent series, Mappings (Mathematics) |
| Journal or Publication Title: | Discrete and Continuous Dynamical Systems. Series B |
| Publisher: | American Institute of Mathematical Sciences |
| ISSN: | 1531-3492 |
| Date: | September 2008 |
| Volume: | Vol.10 |
| Number: | No.2-3 |
| Number of Pages: | 26 |
| Page Range: | pp. 511-536 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Nuffield Foundation, CIC nanoGUNE Consolider (Spain), Catalonia (Spain). Comissió Interdepartamental de Recerca i Innovació Tecnològica |
| Grant number: | EP/C000595/1 (EPSRC), BFM2003-09504-C02-01 (CICNC), MTM2006-05849 (CICNC), 2005 SGR-1028 (CIRIT) |
| Version or Related Resource: | Presented at: International Conference on Dynamical Systems, S'Agaro, Spain, May 29-Jun 03, 2006 |
| Type of Event: | Conference |
| URI: | http://wrap.warwick.ac.uk/id/eprint/29766 |
Data sourced from Thomson Reuters' Web of Knowledge
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