Analytic nilpotent centers as limits of nondegenerate centers revisited

Isaac A. García; Héctor Giacomini; Jaume Giné; Jaume Llibre

doi:https://doi.org/10.1016/j.jmaa.2016.04.046

Analytic nilpotent centers as limits of nondegenerate centers revisited

Isaac A. García, Héctor Giacomini, Jaume Giné, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré-Liapunov method to detect centers with purely imaginary eigenvalues can be used to detect nilpotent centers.

Original language	English
Pages (from-to)	893-899
Journal	Journal of Mathematical Analysis and Applications
Volume	441
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.04.046
Publication status	Published - 15 Sep 2016

Keywords

Nilpotent center
Poincaré-Liapunov constants

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title = "Analytic nilpotent centers as limits of nondegenerate centers revisited",

abstract = "{\textcopyright} 2016 Elsevier Inc. We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincar{\'e}-Liapunov method to detect centers with purely imaginary eigenvalues can be used to detect nilpotent centers.",

keywords = "Nilpotent center, Poincar{\'e}-Liapunov constants",

author = "Garc{\'i}a, {Isaac A.} and H{\'e}ctor Giacomini and Jaume Gin{\'e} and Jaume Llibre",

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AU - García, Isaac A.

AU - Giacomini, Héctor

AU - Giné, Jaume

AU - Llibre, Jaume

PY - 2016/9/15

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N2 - © 2016 Elsevier Inc. We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré-Liapunov method to detect centers with purely imaginary eigenvalues can be used to detect nilpotent centers.

AB - © 2016 Elsevier Inc. We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré-Liapunov method to detect centers with purely imaginary eigenvalues can be used to detect nilpotent centers.

KW - Nilpotent center

KW - Poincaré-Liapunov constants

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U2 - https://doi.org/10.1016/j.jmaa.2016.04.046

DO - https://doi.org/10.1016/j.jmaa.2016.04.046

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SP - 893

EP - 899

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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