Extending to the complex line Dulac’s corner maps of non-degenerate planar singularities

DOI10.1088/0951-7715/28/11/4139zbMath1328.30016arXiv1301.1639OpenAlexW2963907631MaRDI QIDQ3458805

Loïc Teyssier

Publication date: 23 December 2015

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.1639

zbMATH Keywords

holomorphic foliationDulac map

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Singularities of holomorphic vector fields and foliations (32S65) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25) Dynamical aspects of holomorphic foliations and vector fields (37F75) Miscellaneous topics of analysis in the complex plane (30E99)

Cites Work

• Unnamed Item
• Germ of presentable foliations of the complex plane
• Unfolding of resonant saddles and the Dulac time
• Limit cycles of polynomial vector fields with nondegenerate singular points on the real plane
• Topology of singular holomorphic foliations along a compact divisor
• Applications de Dulac et applications pfaffiennes
• Non-accumulation of critical points of the Poincaré time on hyperbolic polycycles
• Reduction of Singularities of the Differential Equation Ady = Bdx

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