Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type
2014 ◽
Vol 24
(08)
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pp. 1440011
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Keyword(s):
We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a two-dimensional torus with a fast frequency vector [Formula: see text], with ω = (1, Ω) where Ω is an irrational number of constant type, i.e. a number whose continued fraction has bounded entries. Applying the Poincaré–Melnikov method, we find exponentially small lower bounds for the maximal splitting distance between the stable and unstable invariant manifolds associated to the invariant torus, and we show that these bounds depend strongly on the arithmetic properties of the frequencies.
2004 ◽
Vol 167
(792)
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pp. 0-0
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2000 ◽
Vol 10
(4)
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pp. 433-476
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2003 ◽
Vol 163
(775)
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pp. 0-0
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Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
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1990 ◽
Vol 333
(1630)
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pp. 209-259
1990 ◽
Vol 10
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pp. 295-318
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2005 ◽
Vol 128
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pp. 2726-2746
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1997 ◽
Vol 24
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pp. 127-140
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2015 ◽
pp. 31-37
2016 ◽
Vol 15
(2)
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pp. 981-1024
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