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| Regions of Applicability of Aubry-Mather Theory for Non-convex Hamiltonian |
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Citation： |
Min ZHOU,Binggui ZHONG.Regions of Applicability of Aubry-Mather Theory for Non-convex Hamiltonian[J].Chinese Annals of Mathematics B,2011,32(4):605~614 |
| Page view： 1721
Net amount： 1762 |
Authors： |
Min ZHOU; Binggui ZHONG; |
Foundation： |
the Graduate Student Research Fellowship of Jiangsu Province of China (No.
CX10B?002Z). |
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| Abstract： |
Herman constructed an autonomous system of two degrees of freedom which
says that in non-convex situations, oscillations do happen and Aubry-Mather Theory cannot
apply (see the results due to W. F. Chen in 1992). In this paper, it is shown that
although the orbits could visit a region far away from the initial point in phase space, they
can only exist in some fixed regions in I = (I1, I2) plane. Moreover, Aubry-Mather Theory
can be applied outside the regions. |
Keywords： |
Twist map, Aubry-Mather Theory, Non-convex Hamiltonian |
Classification： |
37J45, 37J50 |
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