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Sverdlove, Ronald

Vector fields defined by complex functions. (English) Zbl 0431.34034

J. Differ. Equations 34, 427-439 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 12 Documents

MSC:

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

Keywords:

Hamiltonian system; vector fields; theory of quadratic differentials on Riemann surfaces
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\textit{R. Sverdlove}, J. Differ. Equations 34, 427--439 (1979; Zbl 0431.34034)
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References:

[1] Andronov, A.A; Leontovich, E.A; Gordon, I.I; Maier, A.G, Qualitative theory of second-order dynamical systems, (1973), Wiley New York · Zbl 0282.34022
[2] Andronov, A.A; Pontryagin, L.S, Systèmes grossiers, Dokl. akad. nauk SSSR, 14, 247-251, (1937) · Zbl 0016.11301
[3] Brickman, L; Thomas, E.S, Conformal equivalence of analytic flows, J. differential equations, 25, 310-324, (1977) · Zbl 0348.34034
[4] Coleman, C, Equivalence of planar dynamical and differential systems, J. differential equations, 1, 222-233, (1965) · Zbl 0135.30704
[5] Courant, R; Hilbert, D, ()
[6] Forster, H, Über das verhalten der integralkurven einer gewöhnlichen differential-gleichung erster ordnung in der umgebung eines singulären punktes, Math. Z., 43, 271-320, (1938) · JFM 63.0413.01
[7] Hukuhara, M; Kimura, T; Matuda, K, Equations differentielles ordinaires du premier ordre dans le champ complexe, (1961), Mathematical Society of Japan Tokyo · Zbl 0101.30002
[8] Kaplan, W, Analytic first integrals of ordinary differential equations, Comment. math. helv., 47, 205-212, (1972) · Zbl 0247.34008
[9] Kaplan, W, Analytic ordinary differential equations in the large, (), 131-151
[10] Kaplan, W, On partial differential equations of first order, (), 221-231
[11] Nemitskii, V.V; Stepanov, V.V, Qualitative theory of ordinary differential equations, (1960), Princeton Univ. Press Princeton, N. J
[12] Schaeffer, A.C; Spencer, D.C, Coefficient regions for schlicht functions, () · Zbl 0049.06003
[13] Sverdlove, R, Inverse problems for dynamical systems in the plane, (), 499-502
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