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<p>This paper is concerned with the local study of planar reversible non-smooth vector fields. We know that symmetries produce interesting mathematical challenges and play an important part in many applications. In fact, the role of symmetries is essential, both in linear and in nonlinear analysis. From the other side, non-smooth vector fields have become certainly one of the common frontiers between Mathematics and Physics/Engineering. The main goal of the present work is to present topological models for generic <i>k</i>-parameter families of reversible non-smooth vector fields, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40863_2024_487_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\(k=0, 1, 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, defined around typical singularities.</p>

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Generic singularities of planar reversible Filippov vector fields

  • 期刊论文

  • 发表日期：

    2025年4月4日

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  • Felipe Emanoel Chaves,
  • Luis Fernando Mello,
  • Marco Antonio Teixeira

摘要

This paper is concerned with the local study of planar reversible non-smooth vector fields. We know that symmetries produce interesting mathematical challenges and play an important part in many applications. In fact, the role of symmetries is essential, both in linear and in nonlinear analysis. From the other side, non-smooth vector fields have become certainly one of the common frontiers between Mathematics and Physics/Engineering. The main goal of the present work is to present topological models for generic k-parameter families of reversible non-smooth vector fields, \(k=0, 1, 2\) k = 0 , 1 , 2 , defined around typical singularities.