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.
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Editorial Reviews
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"...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
"...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
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Text: English, Portugese (translation)
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First Sentence:
Linear dynamical systems and their discrete counterparts, linear maps, have complete explicit solutions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quantized torus, quantized tori, irreducible circuits, symplectic area, semiclassical wave function, resonant normal form, semiclassical propagator, mean level density, periodic orbit sum, periodic tori, periodic torus, neighbouring orbits, cat map, irrational rotation number, stroboscopic map, homoclinic point, hyperbolic map, periodic orbits, single freedom, stable manifold theorem, ergodic system, semiclassical limit, generic bifurcations, invariant tori, separable system Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Linear dynamical systems and their discrete counterparts, linear maps, have complete explicit solutions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quantized torus, quantized tori, irreducible circuits, symplectic area, semiclassical wave function, resonant normal form, semiclassical propagator, mean level density, periodic orbit sum, periodic tori, periodic torus, neighbouring orbits, cat map, irrational rotation number, stroboscopic map, homoclinic point, hyperbolic map, periodic orbits, single freedom, stable manifold theorem, ergodic system, semiclassical limit, generic bifurcations, invariant tori, separable system Key Phrases - Capitalized Phrases (CAPs): (learn more)
Ozorio de Almeida, Exercise Show New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 16
books:
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15
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- Ergodic Problems of Classical Mechanics (Advanced Book Classics) by V. I. Arnold in Back Matter
- Differential Equations (2nd Edition) by John Polking in Back Matter
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter
- Catastrophe Theory and Its Applications (Dover Books on Mathematics) by Tim Poston in Back Matter
- Topics in Nonlinear Dynamics (AIP conference proceedings) by Jorna in Back Matter
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- Quantum Chaos: Between Order and Disorder by Giulio Casati on page 382, and page 531
- Advances in Atomic, Molecular, and Optical Physics, Volume 53 (Advances in Atomic, Molecular, & Optical Physics) by Gerhard Rempe on page 72
- Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics (Cambridge Monographs on Mathematical Physics) by Terry Gannon in Front Matter
- Quantum Dynamics of Simple Systems: Proceedings of the Forty Fourth Scottish Universities Summer School in Physics, Stirling, August 1994 (Scottish Graduate Series) by G.L Oppo on page 313
- Chaos, Scattering and Statistical Mechanics (Cambridge Nonlinear Science Series) by Pierre Gaspard in Back Matter
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