Zobrazeno 1 - 10
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pro vyhledávání: '"Rousseau, Christiane"'
Autor:
Rousseau, Christiane
The paper studies the generic complex 1-dimensional polynomial vector fields of the form $iP(z)\frac{\partial}{\partial z}$, where $P$ is a polynomial with real coefficients, under topological orbital equivalence preserving the separatrices of the po
Externí odkaz:
http://arxiv.org/abs/2411.09108
Autor:
Godin, Jonathan, Rousseau, Christiane
The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a complete parametr
Externí odkaz:
http://arxiv.org/abs/2407.03287
Autor:
Rousseau, Christiane
We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension~$k$ (i.e.~a fixed point of multiplicity $k+1$) under conjugacy. Such generic unfoldings depend real analytically on $k$ real parameters.
Externí odkaz:
http://arxiv.org/abs/2301.11684
Autor:
Vogt, Thomas, Rousseau, Christiane
Publikováno v:
Mitteilungen der DMV. Mar2020, Vol. 28 Issue 1, p26-29. 4p.
Autor:
Godin, Jonathan, Rousseau, Christiane
We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension 1 (i.e. a double fixed point) under conjugacy. These generic unfolding depend on one real parameter. The classification is done by assign
Externí odkaz:
http://arxiv.org/abs/2105.10348
Autor:
Rousseau, Christiane
When are two germs of analytic systems conjugate or orbitally equivalent under an analytic change of coordinates in the neighborhood of a singular point? A way to answer is to use normal forms. But there are large classes of dynamical systems for whi
Externí odkaz:
http://arxiv.org/abs/2011.12456
Autor:
Klimes, Martin, Rousseau, Christiane
In this note we present variants of Kostov's theorem on a versal deformation of a parabolic point of a complex analytic $1$-dimensional vector field. First we provide a self-contained proof of Kostov's theorem, together with a proof that this versal
Externí odkaz:
http://arxiv.org/abs/2002.08444
Autor:
Godin, Jonathan, Rousseau, Christiane
We investigate the local dynamics of antiholomorphic diffeomorphisms around a parabolic fixed point. We first give a normal form. Then we give a complete classification including a modulus space for antiholomorphic germs with a parabolic fixed point
Externí odkaz:
http://arxiv.org/abs/2001.06428
Autor:
Klimeš, Martin, Rousseau, Christiane
In this paper we introduce geometric tools to study the families of rational vector fields of a given degree over $\mathbb C\mathbb P^1$. To a generic vector field of such a parametric family we associate several geometric objects: a periodgon, a sta
Externí odkaz:
http://arxiv.org/abs/1909.09439
Autor:
Rousseau, Christiane
In this paper we describe the bifurcation diagram of the$2$-parameter family of vector fields $\dot z = z(z^k+\epsilon_1z+\epsilon_0)$ over $\mathbb C\mathbb P^1$ for $(\epsilon_1,\epsilon_0)\in \mathbb C^2$. There are two kinds of bifurcations: bifu
Externí odkaz:
http://arxiv.org/abs/1812.04665