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The following question is related to the Seifert conjecture. Let $M$ be a closed manifold with zero Euler characteristic. Is it true that each homotopy class of nowhere-zero vector fields on $M$ contains a vector field with a finite number of (stable) limit cycles (closed trajectories)? Is it easy to construct? |
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Existence of a vector field with a finite number of limit cycles.The following question is related to the Seifert conjecture. Let $M$ be a closed manifold with zero Euler characteristic. Is it true that each homotopy class of nowhere-zero vector fields on $M$ contains a vector field with a finite number of (stable) limit cycles? Is it easy to construct?
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