# Invariant tori for the Nos\'e Thermostat near the High-Temperature Limit

## TL;DR

This paper proves the existence of invariant tori in Nosé thermostated systems near the high-temperature limit, extending previous results to a broader class of thermostats and complementing earlier findings near the decoupling limit.

## Contribution

It demonstrates the presence of invariant tori for a class of thermostats in the high-temperature regime, broadening the understanding of thermostated Hamiltonian systems.

## Key findings

- Invariant tori exist near the high-temperature limit for Nosé-like thermostats.
- Results hold for systems with smooth periodic potentials of class C^n, n>4.
- Complements prior work on decoupling limit by Legoll, Luskin, and Moeckel.

## Abstract

Let H(q,p) = p^2/2 + V(q) be a 1-degree of freedom mechanical Hamiltonian with a C^n periodic potential V where n>4. The Nos\'e-thermostated system associated to H is shown to have invariant tori near the infinite temperature limit. This is shown to be true for all thermostats similar to Nos\'e's. These results complement the result of Legoll, Luskin and Moeckel who proved the existence of such tori near the decoupling limit.