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Title: On the sharpness of the Rüssmann estimates
Author: Figueras, 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:
It is part of: Communications In Nonlinear Science And Numerical Simulation, 2018, vol. 55, p. 42-55
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ISSN: 1007-5704
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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