Timeline for Rotation number for homeomorphisms of a Lie group other than $S^1$
Current License: CC BY-SA 4.0
11 events
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| Sep 27, 2023 at 19:03 | comment | added | Ali Taghavi | @Alejandro In particular Iam thinking to lifting homeomorphism $f$ to $F$ you point out to.Thanks again for your attention | |
| Sep 27, 2023 at 18:30 | comment | added | Ali Taghavi | @Alejandro Thank you very much for your very interesting comment. I think about its details and also I try to remedy the post. regarding the surjectivity we may add extra assumption "compact connected Lie group" | |
| Sep 26, 2023 at 19:18 | comment | added | Alejandro | @AliTaghavi, I don't see how you can construct the map $F$ for an arbitrary $f$. The exponential map is not even surjective on certain Lie groups. On the other hand, you need to impose some restrictions on the map $f$ in order to guarantee the existence of the limit. For instance, in most of the cases $f$ must be homotopic to the identity. | |
| Sep 12, 2023 at 10:27 | comment | added | Martin M. W. | Here's a recent paper which has references to follow; note that this focuses on the torus case. (I'm not familiar with more general Lie group constructions, but a torus seems like the simplest entry point!) On the rotation sets of generic homeomorphisms on the torus, arxiv.org/abs/1901.00396 | |
| Sep 12, 2023 at 5:40 | comment | added | Ali Taghavi | @MartinM.W. Thank you! could you please give me a reference. I googled "Rotation set" and Lie group simultaneously but I could not find materials in this regard | |
| Sep 12, 2023 at 1:41 | comment | added | Martin M. W. | There's an existing notion of a "rotation set" which might be the generalization you're looking for. You can have more than one limit depending on your choice of $x$. It's already pretty interesting in the case of a torus! | |
| Sep 11, 2023 at 22:19 | history | edited | ThiKu | CC BY-SA 4.0 |
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| Sep 11, 2023 at 21:21 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Sep 11, 2023 at 16:48 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 11, 2023 at 16:45 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Sep 11, 2023 at 16:15 | history | asked | Ali Taghavi | CC BY-SA 4.0 |