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This is a Quantitative Study study.

September 30, 2025Open Access

On the Linearization of Certain Singularities of Nijenhuis Operators

Puntos clave

The linearization problem for Nijenhuis operators is fully solved in dimension two.
This resolution addresses difficulties associated with left-symmetric algebra, specifically 'b_{1, α}'.
Related classical results provide context on the linearization of vector fields and their mappings.
The findings enhance understanding of analytic properties and singular behaviors in mathematical structures.

Resumen

We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in arXiv: 1903. 06411. One case, however, namely the case of left-symmetric algebra b₁, ⏐, proved to be difficult. Here we solve it and, thus, complete the solution of the linearization problem for Nijenhuis operators in dimension two. The problem turns out to be related to classical results on the linearization of vector fields and their monodromy mappings.

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Cite This Study

Andrey Yu. Konyaev (Fri,) studied this question.

synapsesocial.com/papers/68dc1e358a7d58c25ebb16b8 https://doi.org/https://doi.org/10.48550/arxiv.2509.10155

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