New lower bounds of the number of critical periods in reversible centers
type: Item
instance of: scholarly article
title: New lower bounds of the number of critical periods in reversible centers
zbMATH Open document ID: 1481.34044
author: Iván Sánchez-Sánchez
author: Joan Torregrosa
published in: Journal of Differential Equations
publication date: 2021-06-18T00:00:00Z
review text: The main objective of this paper is to find the highest possible lower bound for the maximum number \(C_l(n)\) of local critical periods that can bifurcate from an \(n\)-th degree planar time-reversible system. This problem is completely solved only for the quadratic case \(n = 2\). The main result of the presented work can be formulated as the following lower bounds \(C_l(n) \geq 6\) for \(n = 3\), \(C_l(n) \geq 10\) for \(n = 4\), \(C_l(n) \geq (n^2 + n - 2)/2\) for \(5 \leq n \leq 9\), \(C_l(n) \geq (n^2 + n - 4)/2\) for \(10 \leq n \leq 16\). The main technique for proving the above result is the study of perturbations of reversible holomorphic (isochronous) centers, inside the reversible centers class. More concretely, the authors study the Taylor developments of the period constants with respect to the perturbation parameters.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 7361047
zbMATH Keywords: bifurcation of critical periods
zbMATH Keywords: criticality
zbMATH Keywords: period constants
zbMATH Keywords: period function
zbMATH Keywords: time-reversible centers
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: j.jde.2021.05.013
OpenAlex ID: W3160776333
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DOI: 10.1016/J.JDE.2021.05.013
description: scientific article; zbMATH DE number 7361047