Timeline for The closure of all periodic homeomorphisms of circle
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 17, 2015 at 7:54 | vote | accept | Ali Taghavi | ||
| Jan 14, 2015 at 20:11 | answer | added | Victor Kleptsyn | timeline score: 11 | |
| Jan 14, 2015 at 19:47 | answer | added | Alejandro | timeline score: 4 | |
| Jan 14, 2015 at 17:47 | comment | added | Ryan Budney | The elements that are not in the closure of the periodic elements, they're things like homeomorphisms that have some non-empty fixed-point sets, but the fixed point set is not the entire circle. So on the intervals between the fixed points they're shift operations. | |
| Jan 14, 2015 at 15:14 | comment | added | Alejandro | @AliTaghavi notice that if periodic orbits of $g$ are dense, then $g\in Y$. In fact, any periodic orientation-reversing homeo has period $2$, and hence there is no orientation-reversing map in $\overline{Y}\setminus Y$. On the other hand, every periodic orbit of an orientation-preserving homeo has the same period. So, any $g$ with dense periodic orbits must be periodic itself. | |
| Jan 14, 2015 at 10:37 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 334 characters in body; edited tags
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| Jan 14, 2015 at 10:02 | comment | added | Ali Taghavi | @Hachino Any way, thank you for your comment:) | |
| Jan 14, 2015 at 9:52 | comment | added | Hachino | I don't know, that's just something your question reminded me of. I am no expert in DS, sorry. | |
| Jan 14, 2015 at 9:44 | comment | added | Ali Taghavi | @Hachino thanks for your comment. Is the situation similar to $g=$ irrational rotation? Is there an example of a $g$ for which periodic orbits are dense, in contrast to irrational rotation? Could you please more explain on your comment? | |
| Jan 14, 2015 at 9:40 | comment | added | Hachino | If it is indeed the case that $g$ is a homeomorphism, then this should help you with $2)$. | |
| Jan 14, 2015 at 9:23 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 88 characters in body
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| Jan 14, 2015 at 9:17 | history | asked | Ali Taghavi | CC BY-SA 3.0 |