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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeOct 5th 2011

New stub ergodic theory wanted at measure theory.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeOct 5th 2011

Speaking of this, I had wanted to get my hands on a proof that the shift transformation on the space of irrationals between 0 and 1, which sends a continued fraction $[a_1, a_2, a_3, \ldots]$ to $[a_2, a_3, \ldots]$, is ergodic with respect to the measure $\frac1{\log 2}\frac{d x}{1 + x}$. Any ideas where to find such a proof? (Might be nice for an article ergodic theory as well, since this measure space provides archetypal examples of chaotic phenomena, or so I sense.)

• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeOct 5th 2011
• (edited Oct 5th 2011)

I think that there is an encyclopaedia of mathematics and applications: dynamical systems (red cover, edit: or this was about operator algebras and dynamical systems? edit: no, it is very abstract one, I just peeked into it) which has large part dedicated to the shift-type dynamical systems. I had it in hands years ago, so I can not say about the particular result, but I would not be surprised to find it there.

Edit: I added a link to ergodic theory to one course page having some canonical references in ergodic theory.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 25th 2012

added to ergodic theory this reference which discusses applications of cohomology theory to the subject. This reminded me of David Corfield’s search for cohomological notions in “random” contexts, though maybe it’s not relevant, I am not sure.