Guckenheimer, John; Holmes, Philip Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. (English) Zbl 0515.34001 Applied Mathematical Sciences, 42. New York etc.: Springer-Verlag. XVI, 453 p., 206 figs. (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 26 ReviewsCited in 3662 Documents MSC: 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 37-XX Dynamical systems and ergodic theory 70H05 Hamilton’s equations 34C25 Periodic solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34C29 Averaging method for ordinary differential equations Keywords:attracting motions; strange attractors; chaos; Van der Pol oscillators; Duffing’s equation; Lorenz equations; bouncing ball problem; local bifurcation; center manifold; Hopf bifurcations; averaging; perturbation; Kolmogorov-Arnold-Moser theory; Hamiltonian systems; Poincare maps; global bifurcations; rotation numbers; Lorenz attractor Software:MACSYMA PDF BibTeX XML Full Text: DOI OpenURL