double resonances
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Author(s):  
Xin Jian ◽  
Yinglin Song ◽  
Junhua Gao ◽  
Yuxiao Wang ◽  
Xueru Zhang

2021 ◽  
Vol 54 (17) ◽  
pp. 175110
Author(s):  
Guanghui Yang ◽  
Zixiang Li ◽  
Qianlong Kang ◽  
Kai Guo ◽  
Han Zhang ◽  
...  

Author(s):  
Kaloshin Vadim ◽  
Zhang Ke

This chapter assesses the choice of cohomology and Aubry-Mather type at the double resonance. It begins by choosing cohomology classes for the (unperturbed) slow mechanical system. As in the case of single-resonance, the strategy is to choose a continuous curve in the cohomology space and prove forcing equivalence up to a residual perturbation. To do this, one needs to use the duality between homology and cohomology. The chapter then proves Aubry-Mather type for the perturbed slow mechanical system and reverts to the original coordinates. As the system has been perturbed, one needs to modify the choice of cohomology classes to connect the single and double resonances. Finally, the chapter proves Theorem 2.2, proving the main theorem.


2020 ◽  
Vol 22 (9) ◽  
pp. 095007
Author(s):  
Xinan Xu ◽  
Jinwu Dong ◽  
Shuai Chen ◽  
Xianyu Ao

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