Timeline for Existence of a pair of matrices in SL(2,Z) satisfying certain constraints on the spectral radius
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Dec 14, 2011 at 11:06 | comment | added | Ian Morris | Ian Agol's answer has been incorporated into the article "On a Devil’s staircase associated to the joint spectral radii of a family of pairs of matrices" which will be published in Journal of the European Mathematical Society in late 2012. | |
| Jun 11, 2010 at 12:33 | vote | accept | Ian Morris | ||
| Jun 8, 2010 at 16:53 | answer | added | Ian Agol | timeline score: 10 | |
| Jun 8, 2010 at 16:00 | comment | added | Qiaochu Yuan | Some thoughts. I believe the second condition requires that tr A = tr C^k and tr B = tr C^l for some C in SL(2, Z). If we then write A = C^k + X, B = C^l + Y where X, Y are traceless, the first condition is equivalent to the statement that X C^l + C^k Y + XY has trace zero. I think I can show this is impossible if X = 0. | |
| Jun 8, 2010 at 14:45 | history | asked | Ian Morris | CC BY-SA 2.5 |