Talk:Lyapunov time

what it means

the time for nearby trajectories of the system to diverge by e.

To a layman, "diverge by e" suggests an absolute distance, though there are no units. I was about to change it to something like "the time for a difference between nearby trajectories to increase by a factor of e", but thought best to seek confirmation here first. —Tamfang (talk) 17:26, 17 July 2010 (UTC)

a better statement of this - as a time constant

I think I can describe it better. It is the time constant of the size of the effect of any perturbation, and this includes the effect of the uncertainty of the measurements. The term "time constant" usually being reserved for non-chaotic systems defined by first order linear differential equations, such as charging a capacitor through a resistor (for which the time constant is the resistance times the capacitance - and it's also normally a decaying exponential, whereas this is an increasing one). In other words, if your measurements were to be more precise and accurate by a factor of e, that would only buy you this amount of additional time for which your predictions would be accurate: you could trust your calculations into the future (and reconstruction into the past) by an additional quantity of this amount of time. The "size" of a perturbation may not be easily objectively quantifiable when the perturbation gets amplified by chaos to the extent that the state of the systems with and without the effects of the perturbation bear little resemblance to each other, but at the beginning when the perturbation (or uncertainty due to limitations in measurement) is essentially an infinitessimal, it is meaningful to say it has increased by a factor of e in this amount of time. Especially if the precision is extreme. For instance, if you had 9 digits of precision, as ln(10) is about 2.3, that would mean that whatever predictions you make would very nearly equally reliable for the same system measured accurately with 10 digits of precision but predicted 2.3 of these time constants longer into the future. The magnitudes of the uncertainties in position and momentum of every element in the chaotic system should increase by a factor of e in that time, because that is the factor by which the effects of an infinitessimal perturbation exhibits in that amount of time relative to the course of events if the perturbation had not happened.

75.164.251.184 (talk) 06:18, 24 November 2013 (UTC)

Too technical

Hello all. I have left a tag on this article because it is too difficult for the layman to understand. I know that some people don't like tagging articles, but those people need to remember that I can't fix it myself because it's too complicated to understand! Chase me ladies, I'm the Cavalry (Message me) 18:04, 10 July 2014 (UTC)

This article is not too technical at all. I'm not a professional, and I understood what it's saying in 10 seconds flat. If you don't have a basic background in mechanics or math, or have no interest in chaotic systems, you may not understand it, but in that case I don't think it's the article's responsibility to provide you with an entire high school/college education before explaining this particular point. ChengduTeacher (talk) 10:39, 14 July 2015 (UTC)

Argon examples

What exactly is being predicted here? The trajectories of the individual atoms? I do not have access to the original source; perhaps somebody who does could specify it in the article? — Preceding unsigned comment added by 86.49.8.80 (talk) 13:10, 26 March 2020 (UTC)