“Lyapunov Characteristic Number”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lyapunov Characteristic Number

释义

Lyapunov Characteristic Number

Given a Lyapunov Characteristic Exponent , the corresponding Lyapunov characteristic number is defined as

(1)

For an

-dimensional linear Map,

(2)

The Lyapunov characteristic numbers

, ...,

are the Eigenvalues of the MapMatrix. For an arbitrary Map

(3)

(4)

the Lyapunov numbers are the Eigenvalues of the limit

(5)

where

is the Jacobian

(6)

for all

, the system is not Chaotic. If

and the Map isArea-Preserving (Hamiltonian), the product ofEigenvalues is 1.

See also Adiabatic Invariant, Chaos, Lyapunov Characteristic Exponent

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