Timeline for Dynamic of $SL_2(\mathbb{Z}$) on $\mathbb{C}^2$

9 events

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Oct 30, 2013 at 15:24	comment	added	Barbara Schapira		Sorry, I wrote my comment too fast; it contains many imprecisions. In fact, my first reaction was due to te fact that I was confused by notations $H^2$ and $\mathbb{H}^2$ that I identified in a first reading.
Oct 30, 2013 at 14:51	comment	added	R W		Did you have a chance to notice that the OP asked about the action of $SL(2,\mathbb Z)$? Or do you want to say that in this situation there is no difference between $\mathbb C$ and $\mathbb Z$? If so, then you are definitely wrong.
Oct 30, 2013 at 14:32	comment	added	Barbara Schapira		It seems to me that your answer contains some confusions. The good reference is Ledrappier-Pollicott below. The linear action of SL(2,C) on $C^2$ is (up to some details) the isometric action of SL(2,C) on the space of horospheres of $H^3$. This action is not dissipative, and admits dense orbits for example.(You can replace $\C$ by $\R$ and $\H^3$ by $\H^2$ above)
Oct 22, 2013 at 21:14	comment	added	R W		No-no-no - what I mean is the really trivial action - the one which does nothing.
Oct 22, 2013 at 7:22	comment	added	Selim G		The trivial action of $SL(2,\mathbb{Z})$ on $\mathbb{R}$ is the action by linear fractional transformations ?
Oct 21, 2013 at 17:09	vote	accept	Selim G
Oct 21, 2013 at 16:13	vote	accept	Selim G
Oct 21, 2013 at 16:16
Oct 21, 2013 at 15:09	history	edited	R W	CC BY-SA 3.0	added 73 characters in body
Oct 21, 2013 at 14:55	history	answered	R W	CC BY-SA 3.0