Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONTINUUM-WISE EXPANSIVENESS FOR C1 GENERIC VECTOR FIELDS

  • Manseob Lee (Department of Marketing Big Data Mokwon University)
  • Received : 2022.07.15
  • Accepted : 2022.12.01
  • Published : 2023.09.01
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Abstract

It is shown that every continuum-wise expansive C1 generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C1 generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C1 generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

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References

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