Continuous Limit of Discrete Sawtooth Maps and its Algebraic Framework

TL;DR

This paper investigates the logarithmic time scale in discrete Sawtooth Maps on the 2-torus, using quantum-inspired techniques and localized states to analyze their dynamical properties.

Contribution

It introduces a novel algebraic framework and state-based approach inspired by quantum mechanics to study the dynamics of discrete Sawtooth Maps.

Findings

Identification of a logarithmic time scale in the map dynamics

Development of a quantum-inspired algebraic framework

Use of localized states to analyze dynamical behavior

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.