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Publikováno v:
Moscow Mathematical Journal. 20:375-404
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d76485b08a82c5624561548885d7ba62
https://doi.org/10.17323/1609-4514-2020-2-375-404
https://doi.org/10.17323/1609-4514-2020-2-375-404
Publikováno v:
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena, Elsevier, 2021, 427, pp.133017. ⟨10.1016/j.physd.2021.133017⟩
Physica D: Nonlinear Phenomena, Elsevier, 2021, 427, pp.133017. ⟨10.1016/j.physd.2021.133017⟩
Let F ∈ ℂ [ x , y ] be a polynomial, γ ( z ) ∈ π 1 ( F − 1 ( z ) ) a non-trivial cycle in a generic fiber of F and let ω be a polynomial 1-form, thus defining a polynomial deformation d F + e ω = 0 of the integrable foliation given by F .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7888ef92ad899278b1501dbb491c0880
https://hal.archives-ouvertes.fr/hal-03476651
https://hal.archives-ouvertes.fr/hal-03476651
Publikováno v:
Journal of Dynamical and Control Systems. 25:491-516
We consider germs of holomorphic vector fields in $(\mathbb {C}^{n},0)$ , n ≥ 3, with non-isolated singularities. We assume that the set of singular points forms a submanifold of codimension 2, and the sum of the nonzero eigenvalues of the lineariz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8e87706aac69a62ab0e8939828b30099
https://doi.org/10.1007/s10883-019-09436-7
https://doi.org/10.1007/s10883-019-09436-7
Publikováno v:
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2019, 36 (7), pp.1941-1957. ⟨10.1016/j.anihpc.2019.07.003⟩
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2019, 36 (7), pp.1941-1957. ⟨10.1016/j.anihpc.2019.07.003⟩
In this paper we study polynomial Hamiltonian systems d F = 0 in the plane and their small perturbations: d F + ϵ ω = 0 . The first nonzero Melnikov function M μ = M μ ( F , γ , ω ) of the Poincare map along a loop γ of d F = 0 is given by an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9e877f9a2146712c96356e5d53ed73e3
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02288935
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02288935
Publikováno v:
Bulletin des Sciences Mathématiques
Bulletin des Sciences Mathématiques, Elsevier, 2019, 153, pp.72-85. ⟨10.1016/j.bulsci.2019.02.001⟩
Bulletin des Sciences Mathématiques, Elsevier, 2019, 153, pp.72-85. ⟨10.1016/j.bulsci.2019.02.001⟩
We consider foliations given by deformations d F + ϵ ω of exact forms dF in C 2 in a neighborhood of a family of cycles γ ( t ) ⊂ F − 1 ( t ) . In 1996 Francoise gave an algorithm for calculating the first nonzero term of the displacement func
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::76cc7d7f69901b49d512a2478caae5d6
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02094588/document
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02094588/document
Publikováno v:
Bulletin des Sciences Mathématiques. 163:102896
The purpose of this work is to prove that any analytic class of germs of singular curves in ( C 2 , 0 ) having n + 1 pairwise transversal smooth branches can be realized in an appropriate dicritic foliation with prescribed collection of involutions.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d0a765bffaaa817487d40d117e86eb60
https://doi.org/10.1016/j.bulsci.2020.102896
https://doi.org/10.1016/j.bulsci.2020.102896
Publikováno v:
Moscow Mathematical Journal
Moscow Mathematical Journal, Independent University of Moscow 2018, 18 (2), pp.367-386. ⟨10.17323/1609-4514-2018-18-2-367-386⟩
Moscow Mathematical Journal, Independent University of Moscow 2018, 18 (2), pp.367-386. ⟨10.17323/1609-4514-2018-18-2-367-386⟩
International audience; We consider small polynomial deformations of integrable systems of the form $dF=0, F\in\mathbb{C}[x,y]$ and the first nonzero term $M_\mu$ of the displacement function $\Delta(t,\epsilon)=\sum_{i=\mu}M_i(t)\epsilon^i$ along a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8e01f26219d35989acd79556387492c2
https://hal.archives-ouvertes.fr/hal-01900091
https://hal.archives-ouvertes.fr/hal-01900091
Publikováno v:
Moscow Mathematical Journal. 12:825-862
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cdbda7dc69e4619bbb291e5e55a9bbb2
https://doi.org/10.17323/1609-4514-2012-12-4-825-862
https://doi.org/10.17323/1609-4514-2012-12-4-825-862
Publikováno v:
International Journal of Mathematics. 21:1413-1420
It is proved in Ann. Math. (2)115 (1982) 579–595 that, for any germ of holomorphic nondicritic vector field in (ℂ2, 0), there exists at least one separatrix (invariant analytic curve containing the origin). In Proc. Amer. Math. Soc.125 (1997) 264
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::745fc54944636023947d5bb2ad8d632e
https://doi.org/10.1142/s0129167x10006513
https://doi.org/10.1142/s0129167x10006513