# Problem 117

## Primary tabs

(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 $g$?

## Tags

### 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].

### References

1. [franks1981existence] Franks J, Shub M.  1981.  Topology. 20:273–290.

### MS implies eigen value

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.