Vector fields defined by complex functions

DOI10.1016/0022-0396(79)90029-9zbMath0431.34034OpenAlexW2027748279MaRDI QIDQ1138142

Ronald Sverdlove

Publication date: 1979

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(79)90029-9

zbMATH Keywords

Hamiltonian systemvector fieldstheory of quadratic differentials on Riemann surfaces

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Ordinary differential equations in the complex domain (34M99) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20) Dynamical systems and ergodic theory (37-XX)

Related Items (14)

Piecewise holomorphic systems ⋮ On the separatrix graph of a rational vector field on the Riemann sphere ⋮ Bifurcations in a class of complex differential equations ⋮ On meromorphic complex differential equations ⋮ Global phase portrait and local integrability of holomorphic systems ⋮ Numerical verification method on complex ODEs for existence of global solutions within finite domains ⋮ Gradient systems of harmonic polynomials ⋮ A characterization of multiplicity-preserving global bifurcations of complex polynomial vector fields ⋮ Inverse problems for dynamical systems ⋮ A note on the topological classification of complex polynomial differential equations with only centre singularities ⋮ Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields ⋮ Classification of complex polynomial vector fields in one complex variable ⋮ On the period function for a family of complex differential equations ⋮ Configurations of critical points in complex polynomial differential equations

Cites Work

• Conformal equivalence of analytic flows
• Equivalence of planar dynamical and differential systems
• Analytic first integrals of ordinary differential equations
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