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I hope for some relerant results for the following question: Is the lyapunov exponent continuous with respect to the measure? Assume $M$ is a manifold, $f$ is a diffeomorphism on $M$, $m$ is an invariant measure. Then we have the Lyapunov exponent. Fix $M$ and $f$,is the largest Lyapunov exponent continuous with respect to the weak-* topolpgy on the measure? Do we have any result regarding the linear cocycle?

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  • $\begingroup$ En effet! now fiexd... $\endgroup$
    – leo monsaingeon
    Commented May 22, 2020 at 11:06

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Have a look at the recent survey by Viana

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  • $\begingroup$ thank you very much $\endgroup$
    – jiaming wu
    Commented May 24, 2020 at 2:15

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