Closing Lemma

Let p be a non-wandering point of a diffeomorphism S:M->M of a compact manifold. The closing lemma concerns if S can be arbitrarily well approximated with derivatives of order r for each r by T:M->M so that p is a periodic point of T.

The closing lemma is the 10th of Smale's problems and remains unsettled.

See also

Smale's Problems

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Smale, S. "Mathematical Problems for the Next Century." Math. Intelligencer 20, No. 2, 7-15, 1998.

Cite this as:

Weisstein, Eric W. "Closing Lemma." From MathWorld--A Wolfram Web Resource.

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