“Kolmogorov Entropy”的概念、定义、习题解题方法及翻译-数学辞典

单词

Kolmogorov Entropy

释义

Kolmogorov Entropy

Also known as Metric Entropy. Divide Phase Space into -dimensional Hypercubes ofContent . Let be the probability that a trajectory is in Hypercube at , at , at , etc. Then define

(1)

where

is the information needed to predict which Hypercube the trajectory will be in at

giventrajectories up to

. The Kolmogorov entropy is then defined by

(2)

The Kolmogorov entropy is related to Lyapunov Characteristic Exponents by

(3)

See also Hypercube, Lyapunov Characteristic Exponent

References

Ott, E. Chaos in Dynamical Systems. New York: Cambridge University Press, p. 138, 1993.

Schuster, H. G. Deterministic Chaos: An Introduction, 3rd ed. New York: Wiley, p. 112, 1995.

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