Problem 69Is $h: Diff ^r \to \mathbb{R}$ generically continuous for some $r$?EntropySmoothDynCommentsLedrappier (2016-11-14 16:48:20 -0800 -0800):[newhouse1989continuity] : yes, for $r = \infty $, see [abdenur2011nonuniform] or related stuff for $r =1$?crovisier (2017-06-27 12:23:06 -0700 -0700):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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[newhouse1989continuity] : yes, for $r = \infty $, see [abdenur2011nonuniform] 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.