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单词 PughsClosingLemma
释义

Pugh’s closing lemma


Let f:MM be a 𝒞1 diffeomorphismMathworldPlanetmath of a compact smooth manifold M. Given a nonwandering point x of f, there exists a diffeomorphism g arbitrarily close to f in the 𝒞1 topology of Diff1(M) such that x is a periodic point of g.

The analogous theorem holds when x is a nonwandering point of a 𝒞1 flow on M.

References

  • 1 Pugh, C., An improved closing lemmaMathworldPlanetmath and a general density theorem, Amer. J. Math. 89 (1967).
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