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On the sharpness of the Rüssmann estimates
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Universitat de Barcelona, Departament de Matemàtiques i Informàtica.
Consejo Superior de Investigaciones Científicas, CSIC, Instituto de Ciencias Matemáticas.
2017 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 55, p. 42-55Article in journal (Refereed) Published
Abstract [en]

Estimating the norm of the solution of the linear difference equation u (theta) - u (theta + omega) = v (theta) plays a fundamental role in KAM theory. Optimal (in certain sense) estimates for the solution of this equation were provided by Russmann 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.

Place, publisher, year, edition, pages
2017. Vol. 55, p. 42-55
Keywords [en]
KAM theory, Cohomological equations, Rüssmann estimates, Small divisors
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-336653DOI: 10.1016/j.cnsns.2017.06.021ISI: 000411753200004OAI: oai:DiVA.org:uu-336653DiVA, id: diva2:1166729
Available from: 2017-12-15 Created: 2017-12-15 Last updated: 2017-12-15Bibliographically approved

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Figueras, Jordi-Lluis

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