Invariant tori for multi-dimensional integrable hamiltonians coupled to a single thermostat

Abstract

This paper demonstrates sufficient conditions for the existence of KAM tori in a singly thermostated, integrable hamiltonian system with $n$ degrees of freedom with a focus on the generalized, variable-mass thermostats of order 2--which include the Nosé thermostat, the logistic thermostat of Tapias, Bravetti and Sanders, and the Winkler thermostat. It extends Theorem 3.2 of Legoll, Luskin & Moeckel, (Non-ergodicity of Nosé-Hoover dynamics, Nonlinearity, 22 (2009), pp. 1673--1694) to prove that a "typical" singly thermostated, integrable, real-analytic hamiltonian possesses a positive-measure set of invariant tori when the thermostat is weakly coupled. It also demonstrates a class of integrable hamiltonians, which, for a full-measure set of couplings, satisfies the same conclusion.

32 pages; 7 figures

References in corpus (6)

• Deterministic constant-temperature dynamics for dissipative quantum systems
• The invariant tori of knot type and the interlinked invariant tori in the Nosé-Hoover system
• Analytic Lagrangian tori for the planetary many-body problem
• Nosé-Hoover Dynamics in Quantum Phase Space
• Invariant tori for the Nosé Thermostat near the High-Temperature Limit
• Nosé-Thermostated Mechanical Systems on the n-Torus