Hayashi’s connecting lemma

Let f:MM be a C1 diffeomorphismMathworldPlanetmath of the compact smooth manifold M, and let p,qM be such that there exists a nonperiodic point in ω(p,f)α(q,f) (the intersection of the alpha limit set of q with the omega limit set of p). Then there exists a diffeomorphism g, arbitrarily close to f in the 𝒞1 topology of Diff1(M), such that q is in the forward orbit of p through g, i.e. such that gn(p)=q for some n>0.


  • 1 Wen, L., Xia, Z., C1 connecting lemmas, Trans. Amer. Math. Soc. 352 (2000), no. 11, 5213-5230.
Title Hayashi’s connecting lemma
Canonical name HayashisConnectingLemma
Date of creation 2013-03-22 14:07:16
Last modified on 2013-03-22 14:07:16
Owner Koro (127)
Last modified by Koro (127)
Numerical id 6
Author Koro (127)
Entry type Theorem
Classification msc 37C05
Classification msc 37C25
Synonym connecting lemma