Problem 117
(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 $g$?
(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 $g$?
Comments
I edited this a bit.
The question of what maps on homology can be realized by Morse-Smale diffeomorphisms is addressed in [franks1981existence] .
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.