2,493 reputation
3924
bio website www-irma.u-strasbg.fr/…
location Strasbourg
age 37
visits member for 2 years, 11 months
seen 7 hours ago
I'm working on complex dynamical systems, more specifically on the local/global aspect of singular holomorphic foliations in the complex plane

1d
comment What's the name of this branched covering?
@NoamD.Elkies Yes indeed, thank you for your valuable input. I edited the question accordingly.
1d
revised What's the name of this branched covering?
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2d
revised What's the name of this branched covering?
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2d
asked What's the name of this branched covering?
May
19
comment Characterization of certain analytic vector fields on $S^{2}$
No, you're not missing anything. I just wanted to point out that since your motivation (foliations in $\mathbb P_2(\mathbb C)$) was not dealing with topological conjugacy, maybe you wanted a less general question. That's all…
May
18
comment Characterization of certain analytic vector fields on $S^{2}$
By «orbital equivalence» above I meant to speak of analytical orbital equivalence (=conjugacy), as opposed to topological orbital equivalence (=conjugacy) you speak of. I'm not sure topological equivalence is really what you want, but I can't speak in your stead.
May
18
comment Intrinsic definition of arc length
I don't think your contribution answers the question asked (the OP never said he was scared of parameterizations…) and he probably knows all this. He explicitly stated « without resorting to a parametrization», which is the sole content of your answer. The question was probably intended at a foundational level.
May
18
comment Intrinsic definition of arc length
Am I the only one doubting the research-level relevance of the question (at least in its present form)?
May
18
comment Characterization of certain analytic vector fields on $S^{2}$
I don't quite see why you speak about topological conjugacy in that case. Wouldn't you want something stronger, like orbital equivalence as foliated analytic spaces ? The topological setting destroys far too structure in my opinion, you take the risk of losing rigidity arising from analyticity.In the complex case, there is no such requirement, since all the usual charts on $\mathbb P_2(\mathbb C)$ are birationnally equivalent. This should also be the case in the real setting because stereographic projection is algebraic.
May
17
comment Stability of singularity in singular holomorphic foliation
@AliTaghavi: I'm sorry I have no idea, although it doesn't seem possible at first glance.
May
15
comment Is there a nice “synthetic” way for doing differential geometry on infinite dimensional vector spaces?
I would include the inverse function theorem in what you call "the basic theorems of differential geometry".In that settng even Fréchet manifolds are not sufficient to guarantee it holds...
May
12
comment Algebraic Closure of the field of rational functions
@AllyMath, sorry, I read the sentence too fast.
May
12
comment Algebraic Closure of the field of rational functions
What do you mean by «direct» description? $\bigcup_n\mathbb C((X^{1/n}))$ seems pretty direct to me…
May
12
comment Stability of singularity in singular holomorphic foliation
Yes, you're right, the boundary shape of $W$ should not matter much.
May
11
comment Bounded linear functionals over smooth maps of a compact interval
I fail to see how $||\bullet||_m$ is a norm when $m>1$...?
May
11
reviewed Approve Bounded linear functionals over smooth maps of a compact interval
May
11
comment Stability of singularity in singular holomorphic foliation
@AliTaghavi:I never claimed you could take $V$ as a polydisc, I'm sorry if I was unclear. I modified the post in a way which is clearer I hope. Also, there is no problem in having trajectories with constant $y$-coordinate, they just escape from somewhere else.
May
11
revised Stability of singularity in singular holomorphic foliation
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May
11
comment Stability of singularity in singular holomorphic foliation
In fact every non-singular trajectory escapes from $W$.
May
11
revised Stability of singularity in singular holomorphic foliation
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