An analytic classification of saddle resonant singular points of holomorphic vector fields in the complex plane

DOI10.1007/BF02259621zbMath0988.37066OpenAlexW1978467946MaRDI QIDQ1972707

A. A. Grintchy, Sergey Voronin

Publication date: 13 April 2000

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02259621

zbMATH Keywords

holomorphic vector fieldsanalytic classification\(t\)-monodromysaddle resonant singular points

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Normal forms for dynamical systems (37G05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items

Real-formal orbital rigidity for germs of real analytic vector fields on the real plane, Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle, Extended holonomy and topological invariance of vanishing holonomy group, Analytical classification of saddle-node vector fields., Spectral sequences and parametric normal forms, The moduli space of germs of generic families of analytic diffeomorphisms unfolding of a codimension one resonant diffeomorphism or resonant saddle, Gevrey asymptotics of series in Mourtada-type compensators used for linearization of an analytic \({1:-1}\) resonant saddle, Homological equation and asymptotic cycles of a saddle-node singularity., Analytic classification of saddle nodes

Cites Work

• An ergodic theorem for functions of normal operators
• Complex analytic coordinates in almost complex manifolds
• Problèmes de modules pour des équations différentielles non linéaires du premier ordre
• Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part