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Generically Mañé set supports uniquely ergodic measure for residual cohomology class


Author: Jianlu Zhang
Journal: Proc. Amer. Math. Soc. 145 (2017), 3973-3980
MSC (2010): Primary 37J50; Secondary 70G75
DOI: https://doi.org/10.1090/proc/13581
Published electronically: April 28, 2017
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Abstract: In this paper, we proved that for generic Tonelli Lagrangian, there always exists a residual set $ \mathcal {G}\subset H^1(M,\mathbb{R})$ such that

$\displaystyle \widetilde {\mathcal {M}}(c)=\widetilde {\mathcal {A}}(c)=\widetilde {\mathcal {N}}(c),\quad \forall c\in \mathcal {G}, $

with $ \widetilde {\mathcal {M}}(c)$ supports on a uniquely ergodic measure.

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Additional Information

Jianlu Zhang
Affiliation: Department of Mathematics, University of Toronto, Ontario, Canada
Email: jianlu.zhang@utoronto.ca

DOI: https://doi.org/10.1090/proc/13581
Keywords: Genericity, minimizing measure, Ma\~n\'e set, Tonelli Lagrangian
Received by editor(s): August 27, 2016
Received by editor(s) in revised form: October 14, 2016
Published electronically: April 28, 2017
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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