How Smooth Should be the System Initially to Escape Unbounded Chaos

TL;DR

This paper investigates the initial smoothness required for an infinite harmonic chain to avoid unbounded chaotic behavior, identifying conditions under which particle trajectories remain bounded.

Contribution

It introduces classes of initial conditions that guarantee bounded trajectories in an infinite harmonic chain without stochastic influences.

Findings

Identifies conditions for bounded particle trajectories

Defines classes of initial conditions ensuring stability

Provides theoretical bounds for system behavior

Abstract

We consider infinite harmonic chain on the real line with deterministic dynamics (no stochasticity). We indicate classes of uniformly bounded initial conditions when the trajectories of particles stay uniformly bounded.