Quantum maps are presented with special emphasis on their physical origin. They represent a testing ground for understanding concepts in quantized chaotic systems. The book teaches the modern mathematical methods from analytic and algebraic number theory as applied to quantum maps. It gives a broad and in-depth overview of the mathematical problems arising in this area. Also treated are the numerical aspects in quantum chaos such as eigenvalue and eigenfunctions computations for chaotic quantum systems. The book addresses scientists and advanced students in mathematics and mathematical physics.

Quantum maps are presented with special emphasis on their physical origin. They represent a testing ground for understanding concepts in quantized chaotic systems. The book teaches the modern mathematical methods from analytic and algebraic number theory as applied to quantum maps. It gives a broad and in-depth overview of the mathematical problems arising in this area. Also treated are the numerical aspects in quantum chaos such as eigenvalue and eigenfunctions computations for chaotic quantum systems. The book addresses scientists and advanced students in mathematics and mathematical physics.

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 SchrAdinger 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.

Questo libro ha lo scopo di familiarizzare gli studenti con aspetti anche abbastanza moderni della teoria dei sistemi dinamici facendo quasi del tutto a meno dell'apparato matematico di analisi, algebra e geometria. L'uso della simulazione numerica al calcolatore, sempre piu importante nello studio dei sistemi dinamici, costituisce parte integrante di questo processo. Oltre ad abituare fin da subito gli studenti a mettere le mani sul calcolo scientifico, si mira a far si che la presentazione di questi argomenti possa contribuire a due ulteriori processi formativi di sicuro valore: da una parte, vedere nascere in modo quasi spontaneo concetti matematici profondi e sottili e vederli all'opera nel concreto; dall'altra abituarsi fin da subito a lavorare con la matematica per analizzare quantitativamente le scienze della natura.

Il libro e rivolto agli studenti dei corsi di laurea in matematica, fisica, biologia, ingegneria, ma anche economia, informatica e scienze della comunicazione."