Short chaotic strings and their behaviour in the scaling region

TL;DR

This paper investigates the behavior of short chaotic strings, specifically coupled Chebyshev map lattices, in the scaling region, revealing that their fine structure persists even with minimal lattice points.

Contribution

It demonstrates that the self energy structure of chaotic strings remains intact when the lattice length is reduced to three points in the scaling region.

Findings

Fine structure of self energy is preserved in short chaotic strings.

Behavior of coupled Chebyshev maps is consistent in the scaling region.

Short strings can replicate properties of longer chaotic systems.

Abstract

Coupled map lattices are a paradigm of higher-dimensional dynamical systems exhibiting spatio-temporal chaos. A special case of non-hyperbolic maps are one-dimensional map lattices of coupled Chebyshev maps with periodic boundary conditions, called chaotic strings. In this short note we show that the fine structure of the self energy of this chaotic string in the scaling region (i.e. for very small coupling) is retained if we reduce the length of the string to three lattice points.