Scholarlink

<p>One of the main tools for studying piecewise smooth systems is the regularization process, which generates slow-fast systems. The analysis of these systems heavily relies on the famous Fenichel Theorems, which form the foundation of the Geometric Theory of Singular Perturbations. In this context, our current research focuses on studying slow-fast systems in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {C}^2\)</EquationSource> </InlineEquation>. Specifically, we provide conditions to guarantee the existence of one-dimensional invariant complex manifolds. Consequently, this allows us to establish that the centers, foci, and nodes of the reduced problem are persistent by singular perturbation. The tools used by us are the usual techniques of Fenichel and Briot-Bouquet Theories.</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

On Holomorphic Slow-Fast Systems

  • 期刊论文

  • 发表日期：

    2026年5月26日

查看全文
  • Gabriel Rondón,
  • Paulo R. da Silva,
  • Luiz F. S. Gouveia

摘要

One of the main tools for studying piecewise smooth systems is the regularization process, which generates slow-fast systems. The analysis of these systems heavily relies on the famous Fenichel Theorems, which form the foundation of the Geometric Theory of Singular Perturbations. In this context, our current research focuses on studying slow-fast systems in \(\mathbb {C}^2\) . Specifically, we provide conditions to guarantee the existence of one-dimensional invariant complex manifolds. Consequently, this allows us to establish that the centers, foci, and nodes of the reduced problem are persistent by singular perturbation. The tools used by us are the usual techniques of Fenichel and Briot-Bouquet Theories.