Is $h: Diff ^r \to \mathbb{R}$ generically continuous for some $r$?

[1]: yes, for $r = \infty $, see [2] or related stuff for $r =1$?

Yes also on surfaces for any r>1 (using Katok's horseshoe theorem).

To my knowledge, the case r=1 is open.

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## FL

[1]: yes, for $r = \infty $, see [2] or related stuff for $r =1$?

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## Yes also on surfaces for any

Yes also on surfaces for any r>1 (using Katok's horseshoe theorem).

To my knowledge, the case r=1 is open.

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