Ordinary Differential Equations and Smooth Dynamical Systems |
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analytic vector analytic vector field analytically equivalent asymptotic attractor blow-up called cascade center manifold Chap characteristic trajectory closed phase curves closed trajectory codimension coefficients compact complex components compound cycle connected coordinates corresponding defined Definition denote diffeomorphism differential equations direction field domain dynamical systems eigenvalues equilibrium point finite number fixed point flow g formally equivalent fuchsian function germs of vector homeomorphism homotopy hyperbolic integral curves invariant manifolds limit cycles Lyapunov Lyapunov stability M-S systems Math matrix meromorphic metric monodromy group monodromy map movable critical points N-jet neighbourhood nondegenerate nonresonant obtained orbitally parameter periodic trajectories phase curves phase portrait phase space plane Poincaré Poisson-stable polynomial vector field regular singular point resonant resp Riemann-Hilbert problem rotation number Russian semi-trajectory smooth vector field solution sphere structurally stable subset tangent Theorem theory of differential tion topological classification topologically equivalent torus transversal vector bundle vector field zero