Chaotic Dynamics: An Introduction Based on Classical MechanicsIt 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. |
Contents
4 | 21 |
Regular motion | 51 |
on a slope | 76 |
Driven motion | 90 |
Chaos in dissipative systems | 113 |
Transient chaos in dissipative systems | 191 |
Chaos in conservative systems | 227 |
Chaotic scattering | 264 |
Applications of chaos | 279 |
outlook | 318 |
Numerical solution of ordinary differential equations | 329 |
Solutions to the problems | 342 |
| 370 | |
| 387 | |
Other editions - View all
Chaotic Dynamics: An Introduction Based on Classical Mechanics Tamás Tél,Márton Gruiz Limited preview - 2006 |
Chaotic Dynamics: An Introduction Based on Classical Mechanics Tamás Tél,Márton Gruiz No preview available - 2006 |
Common terms and phrases
advection amplitude asymmetric average Lyapunov exponent baker map basic branch basin boundary basin of attraction bifurcation bouncing Cantor set chaotic attractor chaotic bands chaotic motion chaotic saddle chaotic scattering co-ordinates conservative systems corresponding curve cycle points D₁ determined differential equations dimensionless dissipative driven eigenvalues equation of motion equilibrium example exponential fat fractal finite fixed point flow force fractal dimension friction function given homoclinic homoclinic point hyperbolic point information dimension initial conditions intervals iterations kicked oscillators length limit cycle linear natural distribution non-linear obtained origin P₁ parameter particle pendulum periodic orbits phase portrait phase space phase space volume plane Poincaré Poincaré map position Problem rotation Section slope solution spiral attractor stable and unstable steps stroboscopic map topological entropy tori torus trajectories transient chaos two-cycle two-dimensional Un+1 unit square unstable direction unstable manifold values velocity vertical Xn+1
Popular passages
Page 383 - Nychka, DW (1998). Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling.
Page 385 - The effect of small-scale inhomogeneities on ozone depletion in the Arctic.
Page 384 - Ott, E., Grebogi, C. and Yorke, JA "Controlling Chaos", Phys.
Page 381 - Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling.
Page 384 - Boccaletti, S.. Grebogi, C., Lai, YC., Mancini, H. and Maza, D. 'The control of chaos: theory and applications', Phys. Rep. 329, 103 (2000).
Page 384 - Petrov, V, Gaspar, V, Masere, J. and Showalter, K. 'Controlling chaos in the Belousov-Zhabotinsky reaction'.