2,528 reputation
31025
bio website www-irma.u-strasbg.fr/…
location Strasbourg
age 38
visits member for 3 years, 1 month
seen 9 hours ago

I'm working on complex dynamical systems, more specifically on the local/global aspect of singular holomorphic foliations in the complex plane


10h
reviewed Reject arithmetic progressions with few primes
Jul
10
comment Two limit cycles which lie on the same leaf
Dear Ali, have you tried to write down an example? Can you mention what you have tried so far? I particularly think about the article by Llibre and Rodriguez «Configurations of limit cycles and planar polynomial vector fields» where you encounter explicit examples of planar polynomial vector fields with prescribed topological configuration of limit cycles. I'm sure you can answer one of the two questions you raise here by following the work in the article. But you must mention the effort you provided with respect to your problem!
Jun
26
reviewed Approve A delicate elementary inequality
Jun
22
comment Two vector fields are cojugate but not take orbits
Looks like homework to me...
Jun
20
reviewed Approve Reference request: Intrinsic definition of the strong Whitney topology on $\mathcal{C}^{\infty}(M,\mathbb{R})$ without using charts or jets
Jun
19
comment Classification of complex Kronecker foliations
The additive and multiplicative actions are related through the exponential mapping.
Jun
19
comment Classification of complex Kronecker foliations
Yes, obviously you're right, the torus is the quotient of $\mathbb C^*$.
Jun
19
comment Classification of complex Kronecker foliations
Anyway, the question I understand here is to describe the set of $\theta$ for which the induced foliations are topologically equivalent, right?
Jun
19
comment Classification of complex Kronecker foliations
Well… for $n\in\mathbb Z$ you have a diffeomorphism $x\mapsto x\alpha^n$. Similarly the additive $\mathbb Z^2$-action is given by $(n,m)\cdot x=x+n+m\tau$, which corresponds to $\tau=i$ in your example.
Jun
19
comment Classification of complex Kronecker foliations
You have a multiplicative action $x\mapsto x\alpha$ for $\alpha\neq 0$, for instance, and the quotient is a torus if $\alpha$ is not real. Anyway, I understood that you were speaking about translation, but there still is an ambiguity, as the action of $\mathbb Z^2$ on $\mathbb C$ usually depends on a complex non-real parameter $\tau$.So I take it that $\tau=i$ here.
Jun
19
reviewed No Action Needed Determinant of a Certain Positive-Definite Block Matrix
Jun
19
reviewed Approve Counterexamples to Kollár's conjecture
Jun
19
comment Classification of complex Kronecker foliations
Could you please describe what are those "obvious" actions ? I can think of different ones, and don't know which is the one you refer to.
Jun
19
reviewed Approve Counterexamples to Kollár's conjecture
Jun
16
reviewed Approve Borel subsets of Polish groups
Jun
15
reviewed Approve Non meager rectangle
Jun
13
comment Under what conditions a linear automorphism is an isometry of some norm?
It seems to me that the phenomenon you describe with the matrix $A$ will repeat itself whenever you have a non-diagonalisable endomorphism (over $\mathbb C$).
Jun
11
revised Can every commutative ring of characteristic $p\in\mathbb P$ be written as the form $R/(p)$ with $R$ being a ring of characteristic $0$?
edited title
Jun
11
reviewed Approve Flatness of a simple ring extension
Jun
10
awarded  Nice Answer