Analytic normal forms and inverse problems for unfoldings of 2-dimensional saddle-nodes with analytic center manifold

Autor: Christiane Rousseau, Loïc Teyssier

Publikováno v: Annales Scientifiques de l'École Normale Supérieure
Annales Scientifiques de l'École Normale Supérieure, Société mathématique de France, 2021, 54 (1), pp.133-233. ⟨10.24033/asens.2457⟩

We give normal forms for generic k-dimensional parametric families $(Z_\varepsilon)_\varepsilon$ of germs of holomorphic vector fields near $0\in\mathbb{C}^2$ unfolding a saddle-node singularity $Z_0$, under the condition that there exists a family o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49fb10276c7b0382709043da2c02656d
https://hal.archives-ouvertes.fr/hal-01890315

Coalescing complex planar stationary points

Autor: Loïc Teyssier

Publikováno v: Mathematical Sciences with Multidisciplinary ApplicationsIn Honor of Professor Christiane Rousseau, And In Recognition of the Mathematics for Planet Earth Initiative
B. Toni. Mathematical Sciences with Multidisciplinary Applications In Honor of Professor Christiane Rousseau, And In Recognition of the Mathematics for Planet Earth Initiative, 157, Springer, 2016, Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-319-31323-8_22⟩
Springer Proceedings in Mathematics & Statistics ISBN: 9783319313214

International audience; Among all bifurcation behaviors of analytic parametric families of real planar vector fields, those that stand out most prominently are confluences of distinct stationary points. The qualitative change is so drastic that in so

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f3bf8f97e72edc69d57285df9e0b3af6
https://hal.archives-ouvertes.fr/hal-01170840v4/file/rousseau_survey.pdf

Analytical classification of saddle-node vector fields

Autor: Loïc Teyssier

Publikováno v: Comptes Rendus Mathematique. 336:619-624

We describe the classification of germs of holomorphic saddle-node vector fields Z at (0,0)∈ C 2 , up to analytical change of local coordinates. The classification of saddle-node foliations F Z , obtained by Martinet and Ramis, led to functional mo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7bf58f8d3d569be49b1be8e9ec2923c3
https://doi.org/10.1016/s1631-073x(03)00134-1

Analyticity in spaces of convergent power series and applications

Autor: Loïc Teyssier

Publikováno v: Moscow Mathematical Journal
Moscow Mathematical Journal, Independent University of Moscow 2015, pp.65

International audience; We study the analytic structure of the space of germs of an analytic function at the origin of \ww C^{\times m} , namely the space \germ{\mathbf{z}} where \mathbf{z}=\left(z_{1},\cdots,z_{m}\right) , equipped with a convenient

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f5cc88a83087023d3be59adac96b6622
https://hal.archives-ouvertes.fr/hal-00855142

Germes de feuilletages présentables du plan complexe

Autor: Loïc Teyssier

Publikováno v: Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society
Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society, Springer Verlag, 2015, 46 (2), pp.275-329. ⟨10.1007/s00574-015-0093-y⟩

Soit \(\mathcal{F}\) un germe de feuilletage singulier du plan complexe. Sous l’hypothese que \(\mathcal{F}\) est une courbe generalisee, D. Marin et J.–F. Mattei ont etabli l’incompressibilite de \(\mathcal{F}\) dans un voisinage epointe d’u

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f453cd8dbf924785e943cf55738b6b5a
https://hal.archives-ouvertes.fr/hal-00799548v3/file/feuilletages_presentables.pdf