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http://hdl.handle.net/2445/143058| Title: | On the sharpness of the Rüssmann estimates |
| Author: | Figueras Romero, Jordi-Lluís Haro, Àlex Luque Jiménez, Alejandro |
| Keywords: | Equacions diferencials lineals Sistemes dinàmics complexos Linear differential equations Complex dynamical systems |
| Issue Date: | Feb-2018 |
| Publisher: | Elsevier B.V. |
| 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. |
| Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2017.06.021 |
| It is part of: | Communications In Nonlinear Science And Numerical Simulation, 2018, vol. 55, p. 42-55 |
| URI: | http://hdl.handle.net/2445/143058 |
| Related resource: | https://doi.org/10.1016/j.cnsns.2017.06.021 |
| ISSN: | 1007-5704 |
| Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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| 672367.pdf | 519.73 kB | Adobe PDF | View/Open |
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