Timeline for If there is a dense geodesic, are almost all geodesics equidistributed? Dense?
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| Jul 25, 2014 at 7:28 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Jul 22, 2014 at 12:12 | vote | accept | Vesselin Dimitrov | ||
| Jul 21, 2014 at 20:45 | comment | added | Asaf | In my opinion, the Andre-Oort situation is more analogous to closed horocycles, as the maps involved are Hecke correspondences, which can be thought somehow as $p$-adic analogues of the horocyclic flow. This gives rise to many powerfull techniques of unipotent flows, such as quantitative recurrence, Ratner's theorems and linearization schemes. In my (not complete) point of view, the Andre-Oort case is more similar to the paper by Nimish you've linked to. You somehow translate closed horocyclic periods. Those periods tend to equidistribute simply by mixing of the geodesic flow. | |
| Jul 21, 2014 at 11:40 | answer | added | Benoît Kloeckner | timeline score: 3 | |
| Jul 21, 2014 at 11:04 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Jul 21, 2014 at 10:50 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Jul 20, 2014 at 21:40 | history | edited | Ian Morris |
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| Jul 20, 2014 at 19:56 | answer | added | Asaf | timeline score: 26 | |
| Jul 20, 2014 at 19:42 | comment | added | paul garrett | Might be relevant to add a weaker "question 0" about the limit in your question 1 being what it is for test functions... since, e.g., Weyl's equidistribution criterion's proof seems to need more than mere continuity (though I may be mistaken). | |
| Jul 20, 2014 at 19:38 | history | asked | Vesselin Dimitrov | CC BY-SA 3.0 |