# Problem 54

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$C$-dense* (mixing)* Axiom A flows

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

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## Comments

## The answer to part 9 is known

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

See Plante, J. F.; Thurston, W. P.

Anosov flows and the fundamental group.

Topology11(1972), 147–150.## Add a new comment