Timeline for Minimal elements of minimal R^k actions
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2015 at 11:58 | vote | accept | coudy | ||
| Jul 7, 2010 at 19:38 | answer | added | coudy | timeline score: 4 | |
| Jun 23, 2010 at 18:17 | comment | added | coudy | @Helge. An invariant measure gives a unitary representation of G on $L^2$. Here is a proof of the Pugh-Shub result for $k=1$. Let f be a $g_{t_0}$ invariant function for some $t_0$. Then $F(x) = \int_{0}^{t_0}\ f(g_s(x))\ e^{-2\pi i s/ t_0}\ ds$ is an eigenvector for the flow $g_t$, associated to the eigenvalue $e^{2\pi i/t_0}$. Eigenvectors associated to different eigenvalues are orthogonal. The conclusion follows, assuming $L^2$ is separable. | |
| Jun 23, 2010 at 12:56 | comment | added | Helge | Just out of curiousity: Is the Pugh/Shub argument hard? And can one explain it and explain why it doesn't extend? | |
| Jun 23, 2010 at 8:04 | history | edited | coudy | CC BY-SA 2.5 |
forgot the compactness assumption
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| Jun 23, 2010 at 8:03 | comment | added | coudy | @Dmitri. Yes, sorry, I forgot the compactness assumption. | |
| Jun 23, 2010 at 7:22 | comment | added | Dmitri Panov | Coudy, I guess you should add some condition on $X$, for example that it is compact. I will delit my answer then... | |
| Jun 22, 2010 at 19:00 | history | edited | coudy | CC BY-SA 2.5 |
typo in the title
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| Jun 22, 2010 at 8:39 | history | asked | coudy | CC BY-SA 2.5 |