Measuring Chaos: Is There a Parameter for Chaotic-ness?

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The discussion centers on identifying a parameter that quantifies the chaotic nature of a system. The Lyapunov exponent is highlighted as a key measure, indicating how quickly two initially close states diverge over time. Participants explore whether a 4-body system exhibits greater chaos compared to a 3-body problem. The conversation emphasizes the importance of these metrics in understanding chaotic systems. Overall, the Lyapunov exponent serves as a foundational tool for measuring chaos in various dynamical systems.
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Is there any parameter that represents the chaotic-ness of a system?

For example, can we show that a 4-body system is in general more chaotic than a 3-body problem?

Thank you : )
 
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I believe there are a few possible measures,
The Lyapunov exponent would be one example.
 
Lyaponuv exponent is the basic one; it indicates the rate of divergence of two closely spaced sets of initial conditions.

Claude.
 
I think it's easist first to watch a short vidio clip I find these videos very relaxing to watch .. I got to thinking is this being done in the most efficient way? The sand has to be suspended in the water to move it to the outlet ... The faster the water , the more turbulance and the sand stays suspended, so it seems to me the rule of thumb is the hose be aimed towards the outlet at all times .. Many times the workers hit the sand directly which will greatly reduce the water...

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