On the sharpness of the Rüssmann estimates

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RECERCAT Home > Universitat de Barcelona > Matemàtiques i Informàtica > Articles publicats en revistes (Matemàtiques i Informàtica) > View document

To access the full text documents, please follow this link: http://hdl.handle.net/2445/143058

dc.contributor	Universitat de Barcelona
dc.contributor.author	Figueras, Jordi Lluís
dc.contributor.author	Haro, Àlex
dc.contributor.author	Luque, Alejandro
dc.date	2019-10-24T11:06:54Z
dc.date	2018-02
dc.date	2019-10-24T11:06:55Z
dc.date	info:eu-repo/date/embargoEnd/2020-02-28
dc.identifier.citation	1007-5704
dc.identifier.citation	672367
dc.identifier.uri	http://hdl.handle.net/2445/143058
dc.format	14 p.
dc.format	application/pdf
dc.language.iso	eng
dc.publisher	Elsevier B.V.
dc.relation	Versió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2017.06.021
dc.relation	Communications In Nonlinear Science And Numerical Simulation, 2018, vol. 55, p. 42-55
dc.relation	https://doi.org/10.1016/j.cnsns.2017.06.021
dc.rights	cc-by-nc-nd (c) Elsevier B.V., 2018
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es
dc.subject	Equacions diferencials lineals
dc.subject	Sistemes dinàmics complexos
dc.subject	Linear differential equations
dc.subject	Complex dynamical systems
dc.title	On the sharpness of the Rüssmann estimates
dc.type	info:eu-repo/semantics/article
dc.type	info:eu-repo/semantics/acceptedVersion
dc.description.abstract	Estimating the norm of the solution of the linear difference equation plays a fundamental role in KAM theory. Optimal (in certain sense) estimates for the solution of this equation were provided by Rüssmann in the mid 70's. The aim of this paper is to compare the sharpness of these classical estimates with more specific estimates obtained with the help of the computer. We perform several experiments to quantify the improvement obtained when using computer assisted estimates. By comparing these estimates with the actual norm of the solution, we can analyze the different sources of overestimation, thus encouraging future improvements.

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