Construction of invariant measures supported within the gaps of Aubry–Mather sets
1996 ◽
Vol 16
(1)
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pp. 51-86
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Keyword(s):
AbstractThis paper represents a contribution to the variational approach to the understanding of the dynamics of exact area-preserving monotone twist maps of the annulus, currently known as the Aubry–Mather theory. The method introduced by Mather to construct invariant measures of Denjoy type is extended to produce almost-periodic measures, having arbitrary rationally independent frequencies, and positive entropy measures, supported within the gaps of Aubry–Mather sets which do not lie on invariant curves. This extension is based on a generalized version of the Percival's Lagrangian and on a new minimization procedure, which also gives a simplified proof of the basic existence theorem for the Aubry–Mather sets.
1991 ◽
Vol 65
(3-4)
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pp. 617-643
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1988 ◽
Vol 8
(4)
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pp. 555-584
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Keyword(s):
2016 ◽
Vol 32
(4)
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pp. 1295-1310
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1994 ◽
Vol 73
(4)
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pp. 388-398
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1990 ◽
Vol 10
(2)
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pp. 209-229
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Keyword(s):
1987 ◽
Vol 28
(3)
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pp. 393-400
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