Hamiltonian Systems: Chaos and Quantization
Cambridge University Press, 29 черв. 1990 р. - 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.
Відгуки відвідувачів - Написати рецензію
Не знайдено жодних рецензій.
Інші видання - Показати все
action amplitude approximation Arnold average becomes Berry canonical caustic chaotic chapter circle classical close complex condition consider constant contribution convergence coordinates corresponding curve defined density depends determine discussed dynamical eigenvalues energy equation equilibrium ergodic example Exercise existence field fixed point flow follows freedom given Hamiltonian Hamiltonian systems homoclinic hyperbolic important independent integrable integrable system intersections invariant iterations leads limit linear manifold matrix measure method motion neighbourhood normal form obtain origin pair periodic orbits perturbation phase space plane Poincaré Poincaré map positive presented principle probability problem projection propagator quantization quantum mechanics reduced region resonance respect result satisfies semiclassical separated sequence Show shown side simple single solution stable stationary structurally surface symplectic takes theorem theory tori torus transformation unstable variables vector wave function Wigner function zero