Timeline for Relation between volume entropy and Hausdorff dim of limit set?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3, 2015 at 18:13 | vote | accept | Jerry | ||
| May 30, 2013 at 9:49 | answer | added | Barbara Schapira | timeline score: 5 | |
| May 17, 2013 at 23:44 | comment | added | Jerry | Thanks Misha, the answer is very helpful. While I'll try to look it up in the BCG papers, do you happen to remember in which direction the inequality is, between entropy and dimension, for non-constantly curved manifolds? | |
| May 17, 2013 at 22:33 | comment | added | Misha | See also math.univ-lyon1.fr/~remy/smf_sec_18_09.pdf and references therein. | |
| May 17, 2013 at 22:33 | comment | added | Misha | In this context, limit set is the ideal boundary of the universal cover. Classically, one uses this in the case of Kleinian groups. Then the right formula is that volume entropy equals Hausdorff dimension of the conical limit set of the group (which could be less than dimension of the full limit set). See Nicholls' book "Ergodic theory of discrete groups". Normalization in variable curvature was worked out in papers by Besson, Courtois and Gallot (maybe also Hammenstadt) and you only have an inequality. Equality if I remember correctly is only in curvature -1 case. | |
| May 17, 2013 at 21:42 | comment | added | user5810 | "Hausdorff dim of" what "limit set"? $\:$ | |
| May 17, 2013 at 21:33 | history | asked | Jerry | CC BY-SA 3.0 |