Chaotic Dynamics: An Introduction Based on Classical Mechanics
It has been discovered over the past few decades that even motions in simple systems can have complex and surprising properties. This volume provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior in-depth scientific and mathematical knowledge. Richly illustrated throughout, its examples are taken from classical mechanics whose elementary laws are familiar to the reader. In order to emphasize the general features of chaos, the most important relations are also given in simple mathematical forms, independent of any mechanical interpretation.
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Chaos in dissipative systems
Transient chaos in dissipative systems
advection angular area preserving average Lyapunov exponent baker map basic branch basin boundary basin of attraction bifurcation bouncing Cantor set chaotic attractor chaotic bands chaotic behaviour chaotic motion chaotic saddle chaotic scattering co-ordinates conservative systems corresponding curve cycle points determined differential equations dimensionless dissipative driving eigenvalues equation of motion equilibrium example exponential fat fractal finite fixed point flow force fractal dimension friction frictionless given heteroclinic points homoclinic homoclinic point hyperbolic point information dimension initial conditions intersection intervals iterations kicked oscillators length limit cycle linear natural distribution non-linear obtained origin parabola parameter particle pendulum periodic orbits phase portrait phase space phase space volume plane Poincare position Problem region rotation Section slope solution spiral attractor ss ss ss stability matrix stable and unstable step stroboscopic map structure topological entropy tori torus trajectories transient chaos two-cycle two-dimensional unit square unstable direction unstable manifold values velocity vertical water-wheel
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Page 381 - Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling.
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