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. |
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Índice
| 3 | |
| 24 | |
| 51 | |
Driven motion | 90 |
Chaos in dissipative systems | 113 |
Transient chaos in dissipative systems | 191 |
Chaotic scattering | 264 |
Applications of chaos | 279 |
outlook | 318 |
Numerical solution of ordinary differential equations | 329 |
Solutions to the problems | 342 |
Bibliography | 370 |
Index | 387 |
Outras edições - Ver tudo
Chaotic Dynamics: An Introduction Based on Classical Mechanics Tamás Tél,Márton Gruiz Pré-visualização indisponível - 2006 |
Palavras e frases frequentes
according amplitude appears attraction average baker map bands basin becomes behaviour body boundary branches called Cantor chaos chaotic attractor characteristic close co-ordinates Consequently conservative considered construction continuous corresponding curve cycle defined depends derivative described determined dimension dimensionless direction distance driving dynamics eigenvalues energy entire equation example exist finite fixed point flow follows force fractal fractal dimension friction function given hyperbolic point identical increases initial conditions intervals iterations kicked length Lyapunov exponent mass motion move natural distribution non-linear object observed obtained occur orbits origin oscillator parameter particle pendulum periodic phase space plane position possible present Problem properties region relation represent resolution respectively rotation saddle scattering segment shows similar simple single solution square stable starting steps stretching stroboscopic structure surface trajectories transient typical unit unstable manifold values velocity volume Xn+1
Passagens conhecidas
Página 321 - In the same spirit, therefore, should each type of statement be received; for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits...
Página xiii - The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations.
Página xiii - We have just seen that the complexities of things can so easily and dramatically escape the simplicity of the equations which describe them. Unaware of the scope of simple equations, man has often concluded that nothing short of God, not mere equations, is required to explain the complexities of the world.
Página 182 - I is the moment of inertia of the system with respect to the axis of rotation.
Página 383 - Nychka, DW (1998). Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling.
Página 385 - The effect of small-scale inhomogeneities on ozone depletion in the Arctic.
Página 384 - Ott, E., Grebogi, C. and Yorke, JA "Controlling Chaos", Phys.
Página 381 - Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling.
Página 384 - Boccaletti, S.. Grebogi, C., Lai, YC., Mancini, H. and Maza, D. 'The control of chaos: theory and applications', Phys. Rep. 329, 103 (2000).
Página 384 - Petrov, V, Gaspar, V, Masere, J. and Showalter, K. 'Controlling chaos in the Belousov-Zhabotinsky reaction'.
Informação bibliográfica
| Título | Chaotic Dynamics: An Introduction Based on Classical Mechanics Chaotic Dynamics: An Introduction Based on Classical Mechanics, Márton Gruiz |
| Autores | Tamás Tél, Márton Gruiz |
| Traduzido por | Katalin Kulacsy |
| Ilustrado por | Szilard Hadobas |
| Edição | ilustrada |
| Editora | Cambridge University Press, 2006 |
| ISBN | 0521547830, 9780521547833 |
| Número de páginas | 393 páginas |
| Exportar citação | BiBTeX EndNote RefMan |