Coalescing Complex Planar Stationary Points

DOI10.1007/978-3-319-31323-8_22zbMath1365.34073OpenAlexW2285086062MaRDI QIDQ5270285

Loïc Teyssier

Publication date: 23 June 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-31323-8_22

zbMATH Keywords

saddle-node bifurcationinverse problemnormal formsholomorphic vector fieldsmodulus spaceunfolding of singularities

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Flows on surfaces (37E35)

Cites Work

• Germ of presentable foliations of the complex plane
• Confluence of singularities of nonlinear differential equations via Borel-Laplace transformations
• Examples of non-conjugated holomorphic vector fields and foliations
• Homological equation and asymptotic cycles of a saddle-node singularity.
• Analytic normal forms for convergent saddle-node vector fields
• Problèmes de modules pour des équations différentielles non linéaires du premier ordre
• The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation
• The moduli space of germs of generic families of analytic diffeomorphisms unfolding of a codimension one resonant diffeomorphism or resonant saddle
• Dynamics of automorphism groups of \(\mathbb{C}, 0\)
• Analytical classification of singular saddle-node vector fields
• Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle
• Analyticity in spaces of convergent power series and applications
• Groupes d'automorphismes de $({\bbfC},0)$ et équations différentielles $ydy+\cdots =0$
• Classification of complex polynomial vector fields in one complex variable
• Holonomie et intégrales premières
• Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincar\'e rank 1
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