# Problem 54

## Primary tabs

$C$-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?

## Tags

The answer to part 9 is known to be negative (no zero homotopic orbits) for codimension $1$ Anosov flow,