Scholarlink

<p>We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality, the case of quadratic vector fields is considered in detail.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Integrability of Polynomial Vector Fields and a Dual Problem

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月23日

查看全文
  • Tatjana Petek,
  • Valery G. Romanovski

摘要

We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality, the case of quadratic vector fields is considered in detail.