Synopses & Reviews
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.
"...successfully gives a concise treatment of well-chosen key elements of the field that are suitable for an upper-level graduate physics course." Science"...a well-written introduction to classical and quantum Hamiltonian dynamics..." Mathematical Reviews"...a fine introduction to its subject matter, for both graduate students and researchers young or old." SIAM Review
Hamiltonian Systems outlines the main results in the field, and considers the implications for quantum mechanics.
The study of nonlinear dynamics, and particularly, chaotic systems, is one of the fastest developing areas in physics and applied mathematics. This introduction to the theory of Hamiltonian chaos considers its implications for quantum mechanics as well.
Table of Contents
Preface; 1. Linear dynamical systems; 2. Nonlinear systems; 3. Chaotic systems; 4. Normal forms; 5. Maps of the circle; 6. Integrable and quasi-integrable systems; 7. Torus quantization; 8. Quantization of ergodic systems; 9. Periodic orbits in quantum field theory; References; Index.