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We explore a simple example of a chaotic thermostated harmonic-oscillatorsystem which exhibits qualitatively different local Lyapunov exponents forsimple scale-model constant-volume transformations of its coordinate q andmomentum p : { q,p } --> { (Q/s),(sP) } . The time-dependent thermostatvariable zeta(t) is unchanged by such scaling. The original (q,p,zeta) motionand 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 modelfurnishes a clearcut chaotic time-reversible example showing how and why boththe local Lyapunov exponents and covariant exponents vary with the scale factors .

Why Instantaneous Values of the "Covariant" Lyapunov Exponents Depend upon the Chosen State-Space Scale