  We explore a simple example of a chaotic thermostated harmonic-oscillator
system which exhibits qualitatively different local Lyapunov exponents for
simple scale-model constant-volume transformations of its coordinate q and
momentum p : { q,p } --> { (Q/s),(sP) } . The time-dependent thermostat
variable zeta(t) is unchanged by such scaling. The original (q,p,zeta) motion
and the scale-model (Q,P,zeta) version of the motion are physically identical.
But both the local Gram-Schmidt Lyapunov exponents and the related local
"covariant" exponents change with the change of scale. Thus this model
furnishes a clearcut chaotic time-reversible example showing how and why both
the local Lyapunov exponents and covariant exponents vary with the scale factor
s .
