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In this chapter, the proof of the Theorem 1.1 is completed in detail. The sink and source switch and lower-saddle and upper-saddle switch are proved first. The results of singular hyperbolic flows, inflection-sink, source, and saddle flows, hyperbolic to hyperbolic-secant flows are proved, and the properties of networks of hyperbolic flows, inflection-sink, source, and saddle flows, hyperbolic-to-hyperbolic-secant flows are determined.

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Proof of Theorem 1.1

  • 章节

  • 发表日期：

    2025年

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  • Albert C. J. Luo

摘要

In this chapter, the proof of the Theorem 1.1 is completed in detail. The sink and source switch and lower-saddle and upper-saddle switch are proved first. The results of singular hyperbolic flows, inflection-sink, source, and saddle flows, hyperbolic to hyperbolic-secant flows are proved, and the properties of networks of hyperbolic flows, inflection-sink, source, and saddle flows, hyperbolic-to-hyperbolic-secant flows are determined.