Perturbation estimates of weak KAM solutions and minimal invariant sets for nearly integrable Hamiltonian systems
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- by Qinbo Chen and Min Zhou PDF
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Abstract:
For nearly integrable and Tonelli system \[ H_{\epsilon }=H_0(p)+\epsilon H_1(q,p,t). \quad (q,p,t)\in \mathbb {T}^n\times \mathbb {R}^n\times \mathbb {T},\] we give the perturbation estimates of weak KAM solution $u_{\epsilon }$ with respect to parameter $\epsilon$ and prove the stability of the Mather set $\tilde {\mathcal {M}}_\epsilon$, Aubry set $\tilde {\mathcal {A}}_\epsilon$, Mañé set $\tilde {\mathcal {N}}_\epsilon$ and even the backward (forward) calibrated curves under the perturbation.References
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Additional Information
- Qinbo Chen
- Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu, People’s Republic of China 210093
- Email: qinboChen1990@gmail.com
- Min Zhou
- Affiliation: School of Information Management, Nanjing University, Nanjing, Jiangsu, People’s Republic of China 210093
- Email: minzhou@nju.edu.cn
- Received by editor(s): December 7, 2015
- Received by editor(s) in revised form: March 7, 2016
- Published electronically: June 30, 2016
- Additional Notes: The authors were supported by the National Basic Research Program of China (973 Program) (Grant No. 2013CB834100), the National Natural Science Foundation of China (Grant No. 11171146, Grant No. 11201222) and a program PAPD of Jiangsu Province, China.
- Communicated by: Yingfei Yi
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 201-214
- MSC (2010): Primary 37Jxx, 70Hxx
- DOI: https://doi.org/10.1090/proc/13193
- MathSciNet review: 3565373