Transition to Chaos in Classical and Quantum Mechanics - Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, July 6 - 13, 1991

The Session was intended to give a broad survey of the mathematical problems arising in the chaotic transition of deterministic dynamical systems, both in classical and quantum mechanics.The lectures of Mather and Forni thoroughly cover the area- preserving twist maps, and include an up-to-date version of the Aubry-Mather theory.The lectures of Bellissard describe the quantum aspects: classical limit, localization, spectral properties of the relevant Schrödinger operators and thus represent an exhaus- tive introduction to the mathematics of "quantum chaos". The lectures of Degli Esposti et al. reviews equidistribu- tion of unstable periodic orbits and classical limit of quantized toral symplectomorphisms.

List of contents

Non commutative methods in semiclassical analysis.- Equidistribution of periodic orbits: An overview of classical VS quantum results.- Action minimizing orbits in hamiltomian systems.

Product details

• Authors: J. Bellissard, M. Degli Esposti, G. Forni
• Assisted by: Sandro Graffi (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.07.2009
• EAN: 9783540584162
• ISBN: 978-3-540-58416-2
• No. of pages: 196
• Dimensions: 156 mm x 236 mm x 13 mm
• Weight: 316 g
• Illustrations: VIII, 196 p.
• Series: Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries; Lecture Notes in Mathematics, Volume 1589; Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis