Pugh’s general density theorem

Let $M$ be a compact smooth manifold. There is a residual subset of $\\operatorname{Diff}^{1}(M)$ in which every element $f$ satisfies $\\overline{\\operatorname{Per}(f)}=\\Omega(f)$ .In other words: Generically, the set of periodic points of a $\\mathcal{C}^{1}$ diffeomorphism is dense in its nonwandering set.

Here, $\\operatorname{Diff}^{1}(M)$ denotes the set of all $\\mathcal{C}^{1}$ difeomorphisms from $M$ toitself, endowed with the (strong) $\\mathcal{C}^{1}$ topology.

References

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

单词	PughsGeneralDensityTheorem
释义	Pugh’s general density theorem Let $M$ be a compact smooth manifold. There is a residual subset of $\\operatorname{Diff}^{1}(M)$ in which every element $f$ satisfies $\\overline{\\operatorname{Per}(f)}=\\Omega(f)$ .In other words: Generically, the set of periodic points of a $\\mathcal{C}^{1}$ diffeomorphism is dense in its nonwandering set. Here, $\\operatorname{Diff}^{1}(M)$ denotes the set of all $\\mathcal{C}^{1}$ difeomorphisms from $M$ toitself, endowed with the (strong) $\\mathcal{C}^{1}$ topology. References 1 Pugh, C., An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967).
随便看	C^-algebra homomorphisms are continuous CalgebraHomomorphismsHaveClosedImages C^-algebra homomorphisms have closed images CalgebraHomomorphismsPreserveContinuousFunctionalCalculus C^-algebra homomorphisms preserve continuous functional calculus CalgebrasHaveApproximateIdentities C^-algebras have approximate identities CameronMartinSpace Cameron-Martin space CancellationIdeal cancellation ideal CancellationRing cancellation ring CancellativeSemigroup cancellative semigroup Canonical canonical CanonicalBasis canonical basis CanonicalBasisForSymmetricBilinearForms canonical basis for symmetric bilinear forms CanonicalCorrelation canonical correlation CanonicalFormOfElementOfNumberField canonical form of element of number field