Chaos and integrability in nonlinear dynamics: an introduction
Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics.
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THE DYNAMICS OF DIFFERENTIAL EQUATIONS
CLASSICAL PERTURBATION THEORY
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arbitrary area-preserving maps associated bifurcations canonical transformation chaos Chapter classical mechanics closed orbits coefficients complex computed conservation consider constant coordinates corresponding defined degrees of freedom denotes determined discussed dynamical systems easily eigenvalues elliptic functions energy shell equations of motion ergodic example expansion first-order flow fluid Fourier frequency given Hamilton-Jacobi equation Hamilton's equations Hamiltonian systems Henon hyperbolic fixed point initial conditions intersections invariant curves iterates KdV equation Lagrangian limit cycle linear Lorenz Lyapunov exponents manifold movable movable singularities nonlinear obtained one-dimensional oscillator Painleve Painleve property parameter periodic perturbation phase plane phase space Phys potential problem quadrature quantal quantum mechanical resonance result rotation semiclassical sequence simple singularities soliton solution solved spectrum stable stationary phase strange attractor structure surface of section theorem theory time-dependent tonian tori torus trajectories turbulence twist map unstable variables vector velocity wave wavefunction zero