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Moduli for heteroclinic connections involving saddle-foci and periodic solutions

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  • Dimension three is the lowest dimension where we can find chaotic behaviour for flows and it may be helpful to distinguish in advance ``equivalent'' complex dynamics. In this article, we give numerical invariants for the topological equivalence of vector fields on three-dimensional manifolds whose flows exhibit one-dimensional heteroclinic connections involving either saddle-foci or periodic solutions. Computed as an infinite limit time, these moduli of topological equivalence heavily rely on the behaviour near the invariant saddles. We also present an alternative proof of the Togawa's Theorem.
    Mathematics Subject Classification: Primary: 37C15; Secondary: 37C20, 37C27, 37C29, 37C70.


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