Foliation

Problem 139

Are polynomial growth foliations hyperfinite? Is $W^{ws}$ on $\Sigma ^+_{\{0,1\}}$ Borel hyperfinite?

Problem 114

$det (I - A)$ as a group invariant for the weak foliation $W^{wu}$, seen as a subgroup lying in some $H_m (M, \mathbb S^1)$?

Problem 112

For a hyperbolic attractor $\Lambda$ of dimension $r$, does $W^s(x) \cap \Lambda$contain a disk of dimension $k := r- Dim W^u (x)?$

Problem 83

Unstable foliations of Anosov diffeos are given by some nilpotent group action.

Problem 82

(Plante) A codimension one minimal foliation has at most one invariant measure

Problem 65

Foliation ergodic theory

1. Ambrose Kakutani (in particular, question 39)
2. Does mixing make any sense? (use category, differentiability, $C^\infty$, analytic structure)
3. Averaging procedure difficulties:
• ergodic theorems, existence of invariant measures, ergodic decomposition, unique ergodicity and uniform convergence.
• polynomial growth  ...
4. Look at some specific foliations
5. Plante's stuff on connections with homology
6. Does pointwise entropy make sense?

Problem 52

Define $\Omega$(foliation). Does $h >0$ make sense?

Problem 51

Look for invariant measures of some standard foliations.

Problem 9

Unique ergodicity of $W^u$ for partially Anosov diffeos.