XXVI.—The Universal Integral Invariants of Hamiltonian Systems and Application to the Theory of Canonical Transformations
1948 ◽
Vol 62
(3)
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pp. 237-246
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Keyword(s):
I. Introduction.—Consider a Hamiltonian system of differential equationswhere H is a function of the 2n variables qi and pi involving in general also the time t. For each given Hamiltonian function H the system (1.1) possesses infinitely many absolute and relative integral invariants of every order r = 1,…, 2n, which can all be written out when (1.1) is integrated. Our interest now is not in these integral invariants, which are possessed by one Hamiltonian system, but in those which are possessed by all Hamiltonian systems. Such an integral invariant, which is independent of the Hamiltonian H, is said to be universal.
1924 ◽
Vol 22
(3)
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pp. 325-349
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1925 ◽
Vol 22
(4)
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pp. 510-533
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2009 ◽
Vol 49
(3)
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pp. 474-481
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1965 ◽
Vol 61
(4)
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pp. 889-894
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1928 ◽
Vol 227
(647-658)
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pp. 137-221
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2011 ◽
Vol 47
(8)
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pp. 1110-1115
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