Homological equation and asymptotic cycles of a saddle-node singularity.

DOI10.1016/j.bulsci.2003.10.002zbMath1126.37311OpenAlexW2042530823MaRDI QIDQ707259

Loïc Teyssier

Publication date: 9 February 2005

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2003.10.002

zbMATH Keywords

vector fieldshomological equationasymptotic cycles

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items

Stokes phenomenon and confluence in non-autonomous Hamiltonian systems ⋮ Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle ⋮ On solvability of homological equations in the problem of center manifold approximation ⋮ Doubly-resonant saddle-nodes in (\protect \mathbb{C}^3,0) and the fixed singularity at infinity in Painlevé equations: analytic classification ⋮ On the universal unfolding of vector fields in one variable: a proof of Kostov's theorem ⋮ Examples of non-conjugated holomorphic vector fields and foliations ⋮ Analytic normal forms for convergent saddle-node vector fields ⋮ Analytic classification of saddle nodes ⋮ Coalescing Complex Planar Stationary Points

Cites Work

• Problèmes de modules pour des équations différentielles non linéaires du premier ordre
• Isotropic transformations of germs of holomorphic foliations
• Formal reduction of cuspidal singularities of analytic vector fields
• An analytic classification of saddle resonant singular points of holomorphic vector fields in the complex plane
• Quelques calculs de cohomologie relative
• [https://portal.mardi4nfdi.de/wiki/Publication:4950750 Sur l'int�gration des �quations diff�rentielles holomorphes r�duites en dimension deux]
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