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Part III ›
Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
foundations +9 more results +19 more equations phenomena depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) definition 32.3: Dynamical system, phase space, flow 32.3 Dynamical system… definition 32.7: Conservative and dissipative flows 32.7 Conservative and… definition 32.8: Attractor and basin 32.8 Attractor and ba… definition 32.10: Fixed point 32.10 Fixed point definition 32.11: Lyapunov stability 32.11 Lyapunov stabili… definition 32.12: Linearization 32.12 Linearization definition 32.19: Lyapunov function 32.19 Lyapunov function definition 32.22: Bifurcation 32.22 Bifurcation definition 32.29: Limit cycle 32.29 Limit cycle definition 32.38: Poincaré section and return map 32.38 Poincaré section… definition 32.41: The horseshoe map 32.41 The horseshoe map definition 32.46: The circular restricted three-body problem 32.46 The circular res… definition 32.50: Diophantine frequency vector 32.50 Diophantine freq… proposition 32.4: The flow is a one-parameter group 32.4 The flow is a on… corollary 32.5: Trajectories do not cross 32.5 Trajectories do… theorem 32.6: Evolution of phase volume 32.6 Evolution of pha… theorem 32.13: Linear stability 32.13 Linear stability theorem 32.15: Hartman–Grobman, restated from Part II 32.15 Hartman–Grobman,… proposition 32.17: Classification of planar fixed points 32.17 Classification o… theorem 32.20: Lyapunov's direct method 32.20 Lyapunov's direc… proposition 32.23: Saddle-node bifurcation 32.23 Saddle-node bifu… proposition 32.24: Transcritical and pitchfork bifurcations 32.24 Transcritical an… theorem 32.25: Hopf bifurcation, quoted 32.25 Hopf bifurcation… proposition 32.26: The Hopf normal form 32.26 The Hopf normal… theorem 32.30: Poincaré–Bendixson, restated from Part II 32.30 Poincaré–Bendixs… corollary 32.32: No chaos in a planar flow 32.32 No chaos in a pl… equation 32.4: eq:chaos-linearization eq. (32.4) equation 32.10: eq:chaos-vdp-si eq. (32.10) equation 32.19: eq:chaos-kam-hamiltonian eq. (32.19) equation 32.25: eq:chaos-standard-map eq. (32.25) equation 32.27: eq:chaos-henon-heiles eq. (32.27) equation 32.36: eq:chaos-lorenz eq. (32.36) equation 32.45: eq:chaos-variational eq. (32.45) equation 32.46: eq:chaos-horizon eq. (32.46) equation 32.50: eq:chaos-logistic eq. (32.50) phenomenon 32.35: Self-sustained oscillation 32.35 Self-sustained o… phenomenon 32.37: Frequency demultiplication and the first heard chaos 32.37 Frequency demult… phenomenon 32.58: Regular and chaotic motion coexist 32.58 Regular and chao… phenomenon 32.59: The solar system is chaotic 32.59 The solar system… phenomenon 32.68: Strange attractors 32.68 Strange attracto… phenomenon 32.72: Sensitive dependence on initial conditions 32.72 Sensitive depend… phenomenon 32.87: Universal period doubling 32.87 Universal period… phenomenon 32.97: Turbulence sets in after a few transitions 32.97 Turbulence sets… The chain of Nonlinear Dynamics and Chaos: 43 of 71 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.