The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations
Aus der Reihe
Institute for Nonlinear Science
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Form:Einzelkauf Download
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Sprache:Englisch
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Verlag:Springer New York
Fr. 112.90
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Erscheinungsdatum
17.04.2013
Verlag
Springer New YorkSeitenzahl
551 (Printausgabe)
Dateigröße
41475 KB
Sprache
Englisch
EAN
9781475743524
resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (2.3), we introduce the concept of integrability. A sys tem is integrable if it has as many global constants of the motion as degrees of freedom. The connection between global symmetries and global constants of motion was first proven for dynamical systems by Noether [Noether 1918]. We will give a simple derivation of Noether's theorem in Sect. (2.3). As we shall see in more detail in Chapter 5, are whole classes of systems which are now known to be inte there grable due to methods developed for soliton physics. In Sect. (2.3), we illustrate these methods for the simple three-body Toda lattice. It is usually impossible to tell if a system is integrable or not just by looking at the equations of motion. The Poincare surface of section provides a very useful numerical tool for testing for integrability and will be used throughout the remainder of this book. We will illustrate the use of the Poincare surface of section for classic model of Henon and Heiles [Henon and Heiles 1964].
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