Timeline for Can the topologist's sine curve be realized as a Julia set?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 28 at 12:50 | comment | added | Alexandre Eremenko | KhashF: yes. But I sketched a proof and gave a reference to a stronger result. | |
| May 28 at 2:37 | comment | added | KhashF | @AlexandreEremenko Thanks for your answer. Indeed, once a small piece of the Julia set is a simple curve, the whole Julia set must be path connected by your argument because it is a surjective image of that piece. And we know that is not the case for the topologist's sine curve. | |
| May 27 at 17:58 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| May 27 at 13:22 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| May 26 at 14:16 | comment | added | D.S. Lipham | I see why the Locally Eventually Onto property implies that the Julia set would have to be locally connected if it contains an arc with interior. But I cannot see why it would have to be a simple curve or Joran curve. Could you give a bit more explanation about this? | |
| May 24 at 14:24 | vote | accept | KhashF | ||
| May 24 at 11:52 | history | answered | Alexandre Eremenko | CC BY-SA 4.0 |