Carleman linearization and normal forms for differential systems with quasi-periodic coefficients

We study the matrix representation of Poincaré normalization using the Carleman linearization technique for non-autonomous differential systems with quasi-periodic coefficients. We provide a rigorous proof of the validity of the matrix representation of the normalization and obtain a recursive algor...

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Autor principal: Chermnykh, Sergey V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4987760/
https://www.ncbi.nlm.nih.gov/pubmed/27588240
http://dx.doi.org/10.1186/s40064-016-3015-6
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author Chermnykh, Sergey V.
author_facet Chermnykh, Sergey V.
author_sort Chermnykh, Sergey V.
collection PubMed
description We study the matrix representation of Poincaré normalization using the Carleman linearization technique for non-autonomous differential systems with quasi-periodic coefficients. We provide a rigorous proof of the validity of the matrix representation of the normalization and obtain a recursive algorithm for computing the normalizing transformation and the normal form of the differential systems. The algorithm provides explicit formulas for the coefficients of the normal form and the corresponding transformation.
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spelling pubmed-49877602016-09-01 Carleman linearization and normal forms for differential systems with quasi-periodic coefficients Chermnykh, Sergey V. Springerplus Research We study the matrix representation of Poincaré normalization using the Carleman linearization technique for non-autonomous differential systems with quasi-periodic coefficients. We provide a rigorous proof of the validity of the matrix representation of the normalization and obtain a recursive algorithm for computing the normalizing transformation and the normal form of the differential systems. The algorithm provides explicit formulas for the coefficients of the normal form and the corresponding transformation. Springer International Publishing 2016-08-15 /pmc/articles/PMC4987760/ /pubmed/27588240 http://dx.doi.org/10.1186/s40064-016-3015-6 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Chermnykh, Sergey V.
Carleman linearization and normal forms for differential systems with quasi-periodic coefficients
title Carleman linearization and normal forms for differential systems with quasi-periodic coefficients
title_full Carleman linearization and normal forms for differential systems with quasi-periodic coefficients
title_fullStr Carleman linearization and normal forms for differential systems with quasi-periodic coefficients
title_full_unstemmed Carleman linearization and normal forms for differential systems with quasi-periodic coefficients
title_short Carleman linearization and normal forms for differential systems with quasi-periodic coefficients
title_sort carleman linearization and normal forms for differential systems with quasi-periodic coefficients
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4987760/
https://www.ncbi.nlm.nih.gov/pubmed/27588240
http://dx.doi.org/10.1186/s40064-016-3015-6
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