Problem 15

Primary tabs

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?

Tags

Tags: 
Hyperbolic
Ergodic

Comments

Submitted by Ledrappier on Mon, 11/14/2016 - 11:43

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

Submitted by Ledrappier on Mon, 11/14/2016 - 11:43

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

References

  1. [dolgopyat1998decay] Dolgopyat D.  1998.  On decay of correlations in Anosov flows. Annals of mathematics. 147:357–390.
  2. [dolgopyat1998prevalence] Dolgopyat D.  1998.  Prevalence of rapid mixing in hyperbolic flows. Ergodic theory and dynamical systems. 18:1097–1114.
  3. [stoyanov2001spectrum] Stoyanov L.  2001.  Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows. American Journal of Mathematics. :715–759.

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