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 / Edition 1

by Sandro Graffi, J. Bellissard, M. Degli Esposti, G. Forni

Overview

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.

Product Details

ISBN-13:	9783540584162
Publisher:	Springer Berlin Heidelberg
Publication date:	10/27/1994
Series:	Lecture Notes in Mathematics , #1589
Edition description:	1994
Pages:	196
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table 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.