Understanding Lyaponov Time & Units

[LagrangeEuler]

In wikipedia text Lyaponov time is defined as inverse of the largest Lyapunov exponent. I have some difficulties with the units. Lyaponov exponents are dimensionless? So Lyaponov time is also then dimensionless? Right? How then in wikipedia article we get Lyaponov time in time units? Could you get me some reasonable explanation?

 

[hilbert2]

If the distance between nearby trajectories of a chaotic system grows like $\exp (\lambda t)$, with $\lambda$ the Lyapunov exponent, then $\lambda$ should have dimensions of reciprocal time, shouldn't it? The argument of an exponential function has to be dimensionless, otherwise the terms of the expansion

$\exp (x) = 1 + x + \frac{1}{2}x^2 + \frac{1}{6}x^3 + \dots$

would have different dimensions.

 

[LagrangeEuler]

Thanks. But always in papers, I saw just dimensionless Lyapunov exponents.

 

[hilbert2]

If you're simulating some theoretical dynamical system with a computer program, it doesn't really matter if you set the position coordinates, time and masses to be dimensionless.