An explicit expression of the first Lyapunov and period constants with applications
type: Item
instance of: scholarly article
title: An explicit expression of the first Lyapunov and period constants with applications
zbMATH Open document ID: 0882.34040
author: V. Mañosa
author: Armengol Gasull
author: Antoni Guillamon
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-03-12T00:00:00Z
review text: By using and extending the method and results of a former paper of \textit{A. Gasull} and \textit{R. Prohens} [Rocky Mt. J. Math. 26, No. 1, 135-164 (1996; Zbl 0855.34032)], the authors got explicit expressions of the first three Lyapunov constants \(V_3\), \(V_5\), \(V_7\) and of the first two period constants \(p_2\), \(p_4\) for a general system: \[ \dot z= iz+\sum_{k\geq 2} F_k(z,\overline z),\quad z\in\mathbb{C} \] having the origin \(z= x+iy=0\) as a critical point with pure imaginary eigenvalues. Applications are made to three special polynomial systems and a Lotka-Volterra system. The authors obtain necessary and sufficient conditions for a center or an isochronous center, as well as the maximum order of a weak focus.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34D30
zbMATH DE Number: 1046879
zbMATH Keywords: Lyapunov constants
zbMATH Keywords: focus
zbMATH Keywords: center
zbMATH Keywords: isochronous center
zbMATH Keywords: return map
zbMATH Keywords: periodic constants
zbMATH Keywords: Lotka-Volterra system
reviewed by: Yanqian Ye
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5455
OpenAlex ID: W1992942797
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DOI: 10.1006/JMAA.1997.5455
description: scientific article; zbMATH DE number 1046879