Timeline for Connected set in a filled Julia set
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16 at 20:10 | comment | added | Gari | Yes, I should be more precise. I exclude exceptional polynomials and I do not think that the Julia set can be homeomorphic to an interval if $f$ is not exceptional. However, I realize now that I don't actually know how to prove that. | |
| May 15 at 21:36 | comment | added | KhashF | @Gari Except for cases where the Julia set is homeomorphic to an interval, right? | |
| May 15 at 20:57 | comment | added | Gari | Hi KhashF. Thanks a lot for your comment. In fact, I have been trying to find a reference for Fact 1) and failed so far. Perhaps it is worth posing this as a separate question (?). I also think that if Fact 1) is true one can always find a set $K_N$ as described. | |
| May 15 at 19:37 | history | edited | KhashF | CC BY-SA 4.0 |
Expanded the discussion.
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| May 15 at 6:16 | comment | added | Gari | Yes I agree. Thanks. | |
| May 14 at 12:53 | comment | added | KhashF | @Gari If the answer is negative for a subset $p_1,\dots,p_N$ of points, then there is no bounded Fatou component. | |
| May 14 at 9:13 | comment | added | Gari | Thanks KashF. I have forgotten to exclude that case. I do not understand your remark though. Are you saying that the answer is no if $K$ has not interior point? | |
| May 13 at 23:36 | history | edited | KhashF | CC BY-SA 4.0 |
Expanded the discussion.
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| May 13 at 18:48 | history | answered | KhashF | CC BY-SA 4.0 |