# KAM tori are no more than sticky

## TL;DR

This paper demonstrates through examples that the doubly exponential stability of KAM tori, under Gevrey smooth perturbations of quasi-convex Hamiltonians, is optimal and cannot be improved.

## Contribution

It provides explicit examples confirming the optimality of the known stability bounds for KAM tori under certain smooth perturbations.

## Key findings

- KAM tori exhibit doubly exponential stability.
- The stability bounds for KAM tori are shown to be optimal.
- Examples illustrate the limits of effective stability.

## Abstract

When a Gevrey smooth perturbation is applied to a quasi-convex integrable Hamiltonian, it is known that the KAM invariant tori that survive are sticky, that is, doubly exponentially stable. We show by examples the optimality of this effective stability.