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Abstract <p> One class of polynomial mappings is studied. Any mapping in this class is shown to be a <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3075_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda\)</EquationSource> </InlineEquation>-truncation for some vector <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3075_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda\)</EquationSource> </InlineEquation>. In addition, for each mapping in this class there exists a direction along which this mapping is regular. It is shown that if some infinitely differentiable mapping is representable near the origin as the sum of the mapping under consideration and a perturbation (small in some sense), then this mapping has a continuous inverse function in some neighborhood of the origin. </p>

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On One Class of Regular \(\lambda\)-Truncations and Its Applications to Inverse Functions

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. V. Arutyunov,
  • S. E. Zhukovskiy

摘要

Abstract

One class of polynomial mappings is studied. Any mapping in this class is shown to be a \(\lambda\) -truncation for some vector \(\lambda\) . In addition, for each mapping in this class there exists a direction along which this mapping is regular. It is shown that if some infinitely differentiable mapping is representable near the origin as the sum of the mapping under consideration and a perturbation (small in some sense), then this mapping has a continuous inverse function in some neighborhood of the origin.