Hamiltonian Systems: Chaos and Quantization (Cambridge Monographs on Mathematical Physics) by Alfredo M. Ozorio de Almeida (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “…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 Book Description Hamiltonian Systems outlines the main results in the field, and considers the implications for quantum mechanics. From the Back Cover This text introduces 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 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 starting point for further investigation. The main focus is on periodic orbits and their neighborhood, since this approach is an especially suitable introduction to the implications of the theory of chaos in quantum mechanics discussed in the last three chapters.The book will be valuable to all researchers and graduate students in physics or applied mathematics interested in Hamiltonian chaos and its implications for quantum theory. Read more

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