Hamiltonian Systems: Chaos and QuantizationCambridge University Press, 1988 - 238 стор. This introduction to the theory of Hamiltonian chaos outlines the main results in the field, and goes on to consider implications for quantum mechanics. The study of nonlinear dynamics, and in particular of chaotic systems, is one of the fastest growing and most productive areas in physics and applied mathematics. In its first six chapters, this timely book introduces the theory of classical Hamiltonian systems. The aim is not to be comprehensive but, rather, to provide a mathematical trunk from which the reader will be able to branch out. The main focus is on periodic orbits and their neighbourhood, as this approach is especially suitable as an introduction to the implications of the theory of chaos in quantum mechanics, which are discussed in the last three chapters. |
Зміст
Linear dynamical systems | 3 |
Nonlinear systems | 24 |
Chaotic motion | 48 |
Normal forms | 74 |
Maps on the circle | 100 |
Integrable and quasiintegrable systems | 115 |
Quantum dynamics | 153 |
Torus quantization | 155 |
Quantization of ergodic systems | 181 |
Periodic orbits in quantum mechanics | 208 |
| 232 | |
| 235 | |
Загальні терміни та фрази
action action-angle variables amplitude approximation Arnold average Berry chord bifurcation billiard Birkhoff normal form canonical transformation cat map chaotic motion classical convergence coordinates corresponding defined dense diffeomorphism dynamical system eigenvalues eigenvectors energy shell entropy equation equilibrium ergodic system exponential fixed point freedom Hamiltonian systems Hartman-Grobman theorem homoclinic point hyperbolic integrable system intersections invariant curves invariant tori irrational irreducible circuits iterations Lagrangian surface level curves linear map Lyapunov exponents matrix neighbourhood nonlinear obtain origin oscillations Ozorio de Almeida P₁ pair parameter Peixoto's theorem periodic orbits periodic points perturbation phase space plane Poincaré map Poincaré section quadratic quantization quantum reduced region resonance result rotation number semiclassical limit separatrices sequence shown in fig solution spectrum stable and unstable stable periodic orbits stationary structurally stable symmetry symplectic area tangent torus two-dimensional unstable manifolds variables vector field wave function Weyl x₁ zero др
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