Monodromy and Dulac's problem for piecewise analytical planar vector fields
type: Item
instance of: scholarly article
title: Monodromy and Dulac's problem for piecewise analytical planar vector fields
arXiv ID: 2106.09827
author: C. A. Buzzi
author: Claudio Pessoa
author: J. C. Medrado
published in: Bulletin des Sciences Mathématiques
publication date: 2023-11-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/2106.09827
review text: The piecewise analytical vector fields \(X\) defined by a pair \((X_+, X_-)\), where \(X_+\) and \(X_-\) are analytical vector fields on regions of the plane separated by an analytical curve \(\sum\). The curve \(\sum\) is called switching curve which separates the plane in two regions \(\sum_+\) and \(\sum_-\) having defined on each region the analytical vector fields \(X_+\) and \(X_-\), respectively. In this paper, the authors study the monodromic singular point in \(\sum\) (called \(\sum\)-monodromic singular point) and Dulac's problem of piecewise analytical vector fields \(X\). First, they characterize all \(\sum\)-monodromic singular points of piecewise analytical vector fields \(X\). Then they consider Dulac's problem restricted to piecewise analytical planar vector fields and prove that there is a neighborhood of the \(\sum\)-monodromic singular point free of limit cycles. Their results are interesting and enrich the dynamics of piecewise analytical vector fields.
reviewed by: Kuilin Wu
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 7771501
zbMATH Keywords: piecewise analytical planar vector fields
zbMATH Keywords: monodromic singular point
zbMATH Keywords: Poincaré map
zbMATH Keywords: Lyapunov coefficients
MaRDI profile type: Publication
OpenAlex ID: W3176219187
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DOI: 10.1016/J.BULSCI.2023.103338
description: scientific article; zbMATH DE number 7771501