Timeline for Mixing of geodesic flow and rate of mixing
Current License: CC BY-SA 4.0
13 events
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| Mar 26 at 1:22 | comment | added | Asaf | No, I don't know of any translation of Roblin's book. | |
| Mar 25 at 9:24 | comment | added | User1723 | Also another question out of context. I tried to use Google Translate for this memoir but it seems not effective to translate the entire thing. Do you know any other source where some translated version of this memoir is available/ or essentially the same content available? | |
| Mar 24 at 19:49 | comment | added | Asaf | Roblin's book is a good source, I remember learning about Babillot's argument there. I think it is in chapter 3 or 4, although her argument is qualitative and not quantitative. The argument is just a variant of Hopf's with some ingenious observation about non-arithmeticity of the length spectrum. Khalil's technique is different (basically extending the approaches of Dolgopyat and Liverani). Khalil's paper should be self-contained... | |
| Mar 24 at 19:11 | comment | added | Moishe Kohan | Your group $G$ is probably assumed to be semisimple with finite center. | |
| Mar 24 at 18:47 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 24 at 17:18 | comment | added | User1723 | Just asking out of curiosity. Does Roblin's memoirs deal with any of these mixing stuff? As it's written in French, hard to decode. That's why asking if you have some ideas. | |
| Mar 24 at 16:08 | comment | added | Asaf | Babillot proved mixing of the geodesic flow for the BMS measure. Oh-Edwards proved exponential mixing for geometrically finite surfaces with high enough critical exponents. I think the general geometrically finite case was only recently announced by Khalil. [In the convex cocompact case, the symbolic techniques work well and the result is know before then]. | |
| Mar 24 at 15:39 | history | edited | User1723 | CC BY-SA 4.0 |
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| Mar 24 at 10:22 | history | edited | User1723 | CC BY-SA 4.0 |
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| Mar 24 at 10:21 | comment | added | User1723 | Right sorry BMS measure. Ok, so even for local mixing is there any kind of rate of mixing? Also, can you say some reference where infinite volume case has been considered. | |
| Mar 24 at 1:45 | comment | added | Asaf | P.S. In infinite measure, every ergodic transformation is mixing (as $\mu(A\cap T^{-n}B) = o(1)$ for all $A,B$ of finite volume). One needs to consider local mixing, etc... | |
| Mar 24 at 1:36 | comment | added | Asaf | Do you mean the BMS measure? the PS measure lives on the boundary, not on the homogeneous space itself... | |
| Mar 23 at 18:17 | history | asked | User1723 | CC BY-SA 4.0 |