Continuous Limit of Discrete Sawtooth Maps and its Algebraic Framework

Abstract

We study the presence of a logarithmic time scale in discrete approximations of Sawtooth Maps on the 2--torus. The techniques used are suggested by quantum mechanical similarities, and are based on a particular class of states on the torus, that fulfill dynamical localization properties typical of quantum Coherent States.

LaTeX, 45 pages, 5 figures. Small changes in the content, references added. To appear in J. Math. Phys

References in corpus (5)

• Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model
• Weyl's law and quantum ergodicity for maps with divided phase space
• Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems
• Quantum Dynamical Entropies in Discrete Classical Chaos
• Classical Limit of Quantum Dynamical Entropies

Cited by in corpus (3)

• On the classical limit of quantum mechanics, fundamental graininess and chaos: compatibility of chaos with the correspondence principle
• Quantum dynamical entropies for discrete classical systems: a comparison
• An estimation of the logarithmic timescale in an ergodic dynamics