Problem 54

$C$-dense (mixing) Axiom A flows

1. speed of mixing
2. asymptotic expression for the number of periodic orbits
3. is $\varphi_1$ intrinsically ergodic?
4. direct proof of mixing of measures
5. analogue of $h(f) \geq \log |\lambda| $
6. understand det$(Id - A) $ as an invariant; relation to $\zeta (0)$
7. stability of $C$-density for attractors
8. condition on $g$ so that $\Sigma_A (g) $ is analytically or $C^\infty $ embeddable as a basic set.
9. can a closed orbit of an Anosov flow be null homotopic?