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This chapter presents some results on the asymptotical behavior of the zero section of a vector bundle, specifically in the context of control systems and multi-time semiflows. The results depend on the well-known Fenichel’s uniformity lemma. It is presented a version of this result for control systems and it is applied in the study of the asymptotical behavior of the zero section of a vector bundle.

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Fenichel’s Uniformity Lemma

  • 章节

  • 发表日期：

    2025年

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  • Victor H. L. Rocha,
  • Josiney A. Souza

摘要

This chapter presents some results on the asymptotical behavior of the zero section of a vector bundle, specifically in the context of control systems and multi-time semiflows. The results depend on the well-known Fenichel’s uniformity lemma. It is presented a version of this result for control systems and it is applied in the study of the asymptotical behavior of the zero section of a vector bundle.