“Liouville's Phase Space Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Liouville's Phase Space Theorem

释义

Liouville's Phase Space Theorem

States that for a nondissipative Hamiltonian System, phase space density (the Area between phase spacecontours) is constant. This requires that, given a small time increment ,

(1)

(2)

the Jacobian be equal to one:



			(3)

Expressed in another form, the integral of the Liouville Measure,

(4)

is a constant of motion. Symplectic Maps of Hamiltonian Systems must therefore be Area preserving (and have Determinants equal to 1).

See also Liouville Measure, Phase Space

References

Chavel, I. Riemannian Geometry: A Modern Introduction. New York: Cambridge University Press, 1994.

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