Problem 6

Zeta function for Axiom A flows and systems

1.  topological identification (try 1-dimensional $\Omega $ first); conjugacy invariance of $\zeta (0)$.

2. For $C^\infty $ flows, $\zeta (s) $ has a meromorphic extension to the complex plane.

3. Connection with Laplacian vs. geodesic results; automorphic forms.

4. Anosov actions.