Total destruction of invariant tori for the generalized Frenkel-Kontorova model

TL;DR

This paper demonstrates that in higher-dimensional Frenkel-Kontorova models, invariant tori parameterized by hull functions can be destroyed by small $C^r$ perturbations, highlighting fragility in these systems.

Contribution

It establishes the destruction of invariant tori in generalized Frenkel-Kontorova models under small $C^r$ perturbations for the first time.

Findings

Invariant tori can be destroyed by small perturbations

Destruction occurs in models on higher-dimensional lattices

Results apply for perturbations with $r<1$

Abstract

We consider generalized Frenkel-Kontorova models on higher dimensional lattices. We show that the invariant tori which are parameterized by continuous hull functions can be destroyed by small perturbations in the $C^r$ topology with $r<1$.