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Examples
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Because of this phenomenon, quantities used to characterize classical chaos (such as Lyapunov exponents and fractal dimension) are not well-defined for the equivalent quantum systems.
Quantum Hyperion Sean 2008
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The “Dynamical System” and “Lyapunov Stability” pages in wikipedia are more accurate, with respect to other wikipedia pages on the topic.
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In other word, if you have a three body problem, where one body is a small mass a satellite, then the motion of that body exhibits some randomness over time as measured by a Lyapunov exponent.
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From extrasolar systems found so far the statistics on Lyapunov exponents chaos time parameters of sorts on extrasolar system data does not look very favorable.
If the Earth is Rare, We May Not Hear from ET | Universe Today 2010
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I did my analyses by computing the Lyapunov exponent for a three body system, such as Sun, Jupiter and Earth ignoring other planets, for the chaotic drift of the Earth-like planet.
If the Earth is Rare, We May Not Hear from ET | Universe Today 2010
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This leads to the chaos element to this problem and the existence of a Lyapunov exponent for chaotic drift.
Nailing Down Goldilocks: What's "Just Right" for Exo-Earths? | Universe Today 2010
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In other word, if you have a three body problem, where one body is a small mass a satellite, then the motion of that body exhibits some randomness over time as measured by a Lyapunov exponent.
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The counterexample only holds if the thermodynamic limit (large-N) exists for the distribution of Lyapunov exponents.
Quantum Hyperion Sean 2008
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Quantum fluctuations can be amplified by classical effects with Lyapunov exponents.
Science and Unobservable Things Sean 2008
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Would the value of the classical Lyapunov exponent tell us how long it would take for the pair to diverge?
Quantum Hyperion Sean 2008
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