Timeline for The entire parametrization of leaves of singular holomorphic foliation of $\mathbb{C}P^2$
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2017 at 10:31 | comment | added | Ali Taghavi | Thank you very much for your help and interesting answer. | |
| Sep 10, 2017 at 10:30 | vote | accept | Ali Taghavi | ||
| Sep 10, 2017 at 10:30 | comment | added | Loïc Teyssier | I don't know offhand, but I think it's folklore. Try Il'Yashenko paper on topological rigidity ? I'll try to find a renerence. | |
| Sep 10, 2017 at 10:28 | comment | added | Ali Taghavi | From what reference you read the proof of genericity of hyperbolic leaves of SHFC, as you indicated in your answer?could you please mention that reference? | |
| Sep 10, 2017 at 10:25 | comment | added | Loïc Teyssier | The argument of Alexandre Eremenko works also for $\mathbb P_2(\mathbb C)$ since the argument only regards a bounded disk : if the function were to assume an infinite value on that disc, you could change the target coordinates so that the new function wouldn't. | |
| Sep 10, 2017 at 10:24 | comment | added | Ali Taghavi | I think you are reffering to this already question: mathoverflow.net/questions/237877/… | |
| Sep 10, 2017 at 10:22 | comment | added | Ali Taghavi | I had asked a question for existence of an entire solution for vander pol but in that question I was considering C to C^2 not CP^2. | |
| Sep 10, 2017 at 10:19 | comment | added | Ali Taghavi | To what extent the entire assumption in the paper of Petrovski Landis paper was essential in their proof? Moreover do you have a downloadable version of the Ilyashenko video? | |
| Sep 10, 2017 at 10:19 | comment | added | Loïc Teyssier | In your question you already obtained an example of polynomial vector field with no entire leaf, I don't really know what can be added. Since I don't have Petrovski and Landis paper, I don't know what they claim. | |
| Sep 10, 2017 at 10:17 | comment | added | Loïc Teyssier | But of course ! Why wouldn't it be ? | |
| Sep 10, 2017 at 10:16 | comment | added | Ali Taghavi | So you consider $\gamma(t)=-1/t$ as a an entire holomorphic map from C to CP^1. yes? | |
| Sep 10, 2017 at 10:13 | history | edited | Loïc Teyssier | CC BY-SA 3.0 |
deleted 230 characters in body
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| Sep 10, 2017 at 10:13 | comment | added | Loïc Teyssier | Yes it's the constant vector field to start with but you twist the $y$-component by a homography so that the foliation is no longer linear in the original coordinates. Ok, that's cheating. Please see my edited answer. | |
| Sep 10, 2017 at 10:07 | comment | added | Ali Taghavi | May I ask you to give comment to the linked question, too? Do you have a downladed version of the talk of Ilyashenko? I have difficulity for multiple watching of this video. | |
| Sep 10, 2017 at 10:03 | comment | added | Ali Taghavi | Thank you. The first part of your answer, I think, correspond to the vector field $x'=1, y'=0$ but we require a non linear term.(As I indicated in my question). The second part of your answer is very helpful for me. But am I mistaken to think in the paper of Petrovski landis they wote in the first parts of their paper, "every solution is an entire holomorphic function from C to CP^2.(In their paper AMS translation)? | |
| Sep 10, 2017 at 9:40 | history | answered | Loïc Teyssier | CC BY-SA 3.0 |