使害羞
发表于 2025-3-26 23:11:03
Additional Topics,Liouville’s theorem has its origin in classical mechanics. In its simplified version it gives a necessary and sufficient condition for a flow of homeomor-phisms on an open subset in ℝ. to be volume preserving. Following K. R. Parthasarathy we give this version first, followed by a discussion of its version in classical mechanics.
BOAST
发表于 2025-3-27 03:41:13
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隐士
发表于 2025-3-27 07:29:07
Hindustan Book Agency (India) 2013
珍奇
发表于 2025-3-27 11:57:49
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能得到
发表于 2025-3-27 13:48:43
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模仿
发表于 2025-3-27 18:46:41
,H. Dye’s Theorem, admit Borel cross-sections. We will therefore assume in the rest of this chapter that . and . are free and their orbit spaces do not admit Borel cross-sections. The first important result on orbit equivalence was obtained by H. Dye and the main aim of this chapter is to prove his theorem.
有杂色
发表于 2025-3-28 01:25:08
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出价
发表于 2025-3-28 03:17:06
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外星人
发表于 2025-3-28 09:28:15
Bernoulli Shift and Related Concepts,hift and the related concept of .-automorphism at an elementary level. Bernoulli shifts provide us with examples of mixing measure preserving automorphisms. The discussion here follows closely the exposition in Patrick Billingsley .
小样他闲聊
发表于 2025-3-28 11:18:29
Discrete Spectrum Theorem,ivalent. Let us say that . and . are spectrally isomorphic if . and . are unitarily equivalent. If . and . are spectrally isomorphic and . is ergodic then . is ergodic, because . is ergodic if and only if 1 is a simple eigenvalue of . hence also of ., which in turn implies the ergodicity of .. Simil