A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients
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A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficientsData de publicació
2014-03Editor
American Institute of Mathematical Sciences (AIMS)ISSN
1078-0947; 1553-5231Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8857Versió
info:eu-repo/semantics/acceptedVersionParaules clau / Matèries
Resum
A perturbative procedure based on the Lie-Deprit algorithm of
classical mechanics is proposed to compute analytic approximations to the
fundamental matrix of linear di erential equations with periodic coe cients.
... [+]
A perturbative procedure based on the Lie-Deprit algorithm of
classical mechanics is proposed to compute analytic approximations to the
fundamental matrix of linear di erential equations with periodic coe cients.
These approximations reproduce the structure assured by the Floquet theorem.
Alternatively, the algorithm provides explicit approximations to the Lyapunov
transformation reducing the original periodic problem to an autonomous sys-
tem and also to its characteristic exponents. The procedure is computationally
well adapted and converges for su ciently small values of the perturbation pa-
rameter. Moreover, when the system evolves in a Lie group, the approximations
also belong to the same Lie group, thus preserving qualitative properties of the
exact solution. [-]
Publicat a
Discrete and Continuous Dynamical Systems, 2014, vol. 34, núm. 3Drets d'accés
Copyright © 2015 American Institute of Mathematical Sciences.
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical System following peer review. The definitive publisher-authenticated version Discrete and Continuous Dynamical Systems, 2014, vol. 34, number 3, pp. 959 - 975 is available online at: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8857
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