Timeline for Dynamical systems with multidimensional, complex and other exotic kinds of time spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2012 at 6:42 | comment | added | Pablo Shmerkin | Qfwfq and Asaf - Good points, I have deleted my last paragraph. | |
| Aug 21, 2012 at 6:41 | history | edited | Pablo Shmerkin | CC BY-SA 3.0 |
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| Aug 20, 2012 at 14:54 | comment | added | Asaf | @Pablo, when the acting group is complex Lie group (and it acts in holomrphic manner), one param. groups are actually 2-dimensional real Lie groups. Because you've discussed homogeneous dynamics, for example the unipotent action in say $\Gamma\backslash SL_{2}(\mathbb{C})$ is a 1-dimensional complex action which can be identified with a 2-dimensional real action (by looking at $SO(3,1)$ and action of 2-dimensional horoballs etc.). | |
| Aug 20, 2012 at 14:19 | comment | added | Qfwfq | I don't agree with your last paragraph (or I misunderstood it). When one looks at maps holomorphic also in the time parameter, he is not considering the multiplicative structure of $\mathbb{C}$, rather he is viewing $\mathbb{C}$ as a $1$-dimensional complex Lie group (rather than just an abstract group) acting holomorphically on the phase space which is a complex manifold. I think it could the "right" thing to do in many cases, for example in the case of holomorphic ODEs | |
| Aug 20, 2012 at 10:59 | history | edited | Pablo Shmerkin | CC BY-SA 3.0 |
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| Aug 20, 2012 at 6:07 | history | answered | Pablo Shmerkin | CC BY-SA 3.0 |