Problem 15

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Renewal theorems for dependent random variables.

1.  Derive as a motivation for Axiom A flow mixingness
2.  How fast is the mixing for Axiom A flows?

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FL

I suppose he meant speed or quality of mixing, but I like this word!

FL

Somehow understood now: see [1], [2],[3] among others. Nice to have a short survey here as well!

References

1. [dolgopyat1998decay] Dolgopyat D.  1998.  Annals of mathematics. 147:357–390.
2. [dolgopyat1998prevalence] Dolgopyat D.  1998.  Ergodic theory and dynamical systems. 18:1097–1114.
3. [stoyanov2001spectrum] Stoyanov L.  2001.  American Journal of Mathematics. :715–759.