Problem 117

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(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 $g$?


I edited this a bit.

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


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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