Order in extremal trajectories

TL;DR

This paper investigates how large deviations in chaotic systems influence trajectory behavior, revealing that such deviations tend to select periodic or quasiperiodic orbits, with implications for understanding complex systems like glasses.

Contribution

It demonstrates that large deviation constraints in chaotic systems select isolated periodic or quasiperiodic trajectories, providing insight into the structure of irregular orbits.

Findings

Large deviations select periodic or quasiperiodic orbits.

Analysis conducted on the baker's map as a representative chaotic system.

Implications discussed for dynamical systems and glassy materials.

Abstract

Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical chaotic system, the baker's map. We show that, out of all irregular trajectories, a large-deviation requirement selects (isolated) orbits that are periodic or quasiperiodic. We discuss what the relevance of this calculation may be for dynamical systems and for glasses.