(Sullivan) Show that $|\lambda| = 1$ for $f: M \to M$, where $f$ is $C^1$ and distal and $\lambda $ is an eigenvalue of $f_\ast$. Is $f \sim g$ for some Morse Smale $g$?

PermalinkSubmitted by DennisSullivan on Tue, 12/27/2016 - 19:40

MS implies eigen value statements

the question is: up to isotopy does the converse hold in the distal case.

remark: for what its worth

in my paper " infinitesimal computations in topology" it is shown that up to isotopy not every diffeo is a composition of morse smale.[uses algebraic group theory] but this is true for surfaces.

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## BHM

I edited this a bit.

## JMF

The question of what maps on homology can be realized by Morse-Smale diffeomorphisms is addressed in [1].

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## MS implies eigen value

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