Two-parameter unfolding of a parabolic point of a vector field in \(\mathbb{C}\) fixing the origin

DOI10.5802/AFST.1669zbMath1483.37059arXiv1812.04665OpenAlexW3164631095MaRDI QIDQ2046370

Christiane Rousseau

Publication date: 17 August 2021

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04665

zbMATH Keywords

bifurcation diagrambifurcations of homoclinic loopsbifurcations of parabolic points

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Singularities of holomorphic vector fields and foliations (32S65) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25)

Cites Work

• Unnamed Item
• Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle
• Generic 2-parameter perturbations of parabolic singular points of vector fields in ℂ
• Analytic moduli for unfoldings of germs of generic analytic diffeomorphisms with a codimension parabolic point
• The Bifurcation Diagram of Cubic Polynomial Vector Fields on CP¹

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