A generalization of the Liouville–Arnol'd theorem
1995 ◽
Vol 117
(2)
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pp. 353-370
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AbstractWe show that the Liouville-Arnol'd theorem concerning knowledge of involutory first integrals for Hamiltonian systems is available for any system of second order ordinary differential equations. In establishing this result we also provide a new proof of the standard theorem in the setting of non-autonomous, regular Lagrangian mechanics on the evolution space ℝ × TM of a manifold M. Both the original theorem and its generalization rely on a certain bijection between symmetries of the system and its first integrals. We give two examples of the use of the theorem for systems on ℝ2 which are not Euler-Lagrange.
2011 ◽
Vol 18
(sup1)
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pp. 237-250
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Keyword(s):
2013 ◽
Vol 82
(1)
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pp. 17-30
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Keyword(s):
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2009 ◽
Vol 16
(sup1)
◽
pp. 209-222
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Keyword(s):
2010 ◽
Vol 2010
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pp. 1-13
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2011 ◽
Vol 44
(24)
◽
pp. 245201
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Keyword(s):
2009 ◽
Vol 23
(30)
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pp. 3659-3666
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2005 ◽
Vol 461
(2060)
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pp. 2451-2477
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