Nonsmoothable, unstable group actions

Pixton, Dennis

doi:10.1090/S0002-9947-1977-0438397-0

Nonsmoothable, unstable group actions
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Trans. Amer. Math. Soc. 229 (1977), 259-268 Request permission

Abstract:

For $k > 1$ there is a nonempty open set of ${C^1}$ actions of ${{\mathbf {Z}}^k}$ on ${S^1}$, no element of which is either topologically conjugate to a ${C^2}$ action or structurally stable. The ${C^1}$ closure of this set contains all ${C^2}$ actions which have compact orbits, so no such action is structurally stable in the space of ${C^1}$ actions.

References

Sur les courbes définies par les équations différentielles à la surface du tore

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