Document type
ArticleVersion
Accepted versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/143058
On the sharpness of the Rüssmann estimates
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
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.
Subject (English)
Citation
Citation
FIGUERAS ROMERO, Jordi-Lluís, HARO, Àlex and LUQUE JIMÉNEZ, Alejandro. On the sharpness of the Rüssmann estimates. Communications In Nonlinear Science And Numerical Simulation. 2018. Vol. 55, num. 42-55. ISSN 1007-5704. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/143058