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 trajectory codimension coefficients compact complex components compound cycle connected coordinates corresponding critical points defined Definition denote diffeomorphism differential equations direction field domain dynamical systems eigenvalues Elementary Singular Points 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 flow M-S systems Math matrix metric monodromy map Morse index motions N-jet n-tuple neighbourhood nondegenerate nonresonant normal form obtained orbitally parameter periodic trajectories phase curves phase portrait phase space plane Poincaré Poisson-stable resonant resp Riemann-Hilbert problem rotation number Russian semi-trajectory smooth DSs smooth vector field solution structurally stable subset tangent Theorem theory of differential tion topological classification topologically equivalent torus transversal vector bundle vector field zero