Aubry-Mather type at the single resonance
This chapter proves Aubry-Mather type in the single-resonance regime. It proves that for a single-resonance normal form system which satisfies the non-degeneracy conditions, every c in the resonance curve is of either Aubry-Mather or bifurcation Aubry-Mather type. The main results are Theorems 9.3 and 9.5, which restate Propositions 3.9 and 3.10. The chapter then proves that the conditions hold on an open and dense set of Hamiltonians. It discusses bifurcations in the double maxima case, as well as hyperbolic coordinates. The chapter also examines normally hyperbolic invariant cylinder, the localization of the Aubry and Mañé sets, and the genericity of the single-resonance conditions.
1969 ◽
Vol 27
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pp. 6-7
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2012 ◽
Vol 132
(8)
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pp. 698-699
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