A Understanding Lyaponov Time & Units

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Lyapunov time is defined as the inverse of the largest Lyapunov exponent, which is typically considered dimensionless. However, there is confusion regarding its units, as some sources present Lyapunov time in time units. The discussion highlights that if the growth of distance between trajectories in a chaotic system is modeled as exp(λt), then λ must have dimensions of reciprocal time to maintain dimensional consistency. Despite the theoretical implications, many papers report Lyapunov exponents as dimensionless, suggesting that in practical simulations, the choice of units may not significantly impact the results. The conversation emphasizes the need for clarity in understanding the relationship between Lyapunov exponents and their units in chaotic systems.
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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?
 

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