Chaotic Dynamics of Nonlinear SystemsAn introduction to the study of chaotic systems via numerical analysis, this work includes many applications in physics and employs differential equations, linear vector spaces and some Hamiltonian systems. Includes problems. |
Contents
Introduction | 1 |
OneDimensional Maps | 13 |
Universality Theory | 33 |
Copyright | |
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Common terms and phrases
area-preserving attracting set center manifold chaotic dynamics chapter computation consider constant coordinates corresponding curves cycle elements damped pendulum dcap defined denote Df(x differential equations digits discussed disk dynamo dynamical system eigenvalues eigenvectors example Feigenbaum FIGURE finite fixed point flip bifurcation flow fractal dimension frequency given Hénon map Hopf bifurcation initial conditions initial point integrable intermittency intersection iterations laminar phase limit cycle linear logistic map Lorenz system Lyapunov exponent LZ complexity map parameter measure nonlinear obtain one-dimensional maps period-doubling periodic orbit perturbation phase space Phys plot Poincaré map Poincaré section random refer renormalization resonance scaling self-similar sequence shows simple pendulum sketch stable string supercycle surface tent map theorem trajectory transformation transistion to chaos trapping region two-dimensional maps universal function unstable manifold variables vector field Xn+1 zero