A topological version of a theorem of Mather on twist maps
1984 ◽
Vol 4
(4)
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pp. 585-603
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Keyword(s):
AbstractIn this report we show that a twist map of an annulus with a periodic point of rotation number p/q must have a Birkhoff periodic point of rotation number p/q. We use topological techniques so no assumption of area-preservation or circle intersection property is needed. If the map is area-preserving then this theorem andthe fixed point theorem of Birkhoff imply a recent theorem of Aubry and Mather. We also show that periodic orbits of (significantly) smallest period for a twist map must be Birkhoff.
2001 ◽
Vol 27
(11)
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pp. 701-706
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Keyword(s):
2012 ◽
Vol 3
(2)
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pp. 305-307
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2016 ◽
Vol 2017
(1)
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pp. 17-30
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2015 ◽
Vol 3
(2)
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pp. 173-182
Keyword(s):
Keyword(s):
2020 ◽
Vol 9
(7)
◽
pp. 4353-4361
Keyword(s):
2020 ◽
Vol 9
(8)
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pp. 5593-5600