Generically Mañé set supports uniquely ergodic measure for residual cohomology class

Zhang, Jianlu

doi:10.1090/proc/13581

Generically Mañé set supports uniquely ergodic measure for residual cohomology class
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Proc. Amer. Math. Soc. 145 (2017), 3973-3980 Request permission

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 \[ \widetilde {\mathcal {M}}(c)=\widetilde {\mathcal {A}}(c)=\widetilde {\mathcal {N}}(c),\quad \forall c\in \mathcal {G}, \] with $\widetilde {\mathcal {M}}(c)$ supports on a uniquely ergodic measure.

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