Thermostated harmonic oscillator dynamics admit phase-space descriptions that are simultaneously expanding, incompressible, or contracting in 3D and 4D models while obeying Liouville's continuity equation.
Nos\'e, ``A Molecular Dynamics Method for Simulations in the Canonical Ensemble'', Molecular Physics 52 , 255-268 (1984)
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Aspects of Nos\'e and Nos\'e-Hoover Dynamics Elucidated
Thermostated harmonic oscillator dynamics admit phase-space descriptions that are simultaneously expanding, incompressible, or contracting in 3D and 4D models while obeying Liouville's continuity equation.