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Jan 27, 2022 at 14:09 comment added YCor I guess the problem with polynomial automorphisms of $\mathbf{R}^n$, with conjugacy in the homeomorphism group, is open as well (in high dimension, maybe in all dimensions $\ge 4$).
Apr 29, 2010 at 12:32 history answered Vladimir Dotsenko CC BY-SA 2.5