Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nonsmoothable, unstable group actions

Author: Dennis Pixton
Journal: Trans. Amer. Math. Soc. 229 (1977), 259-268
MSC: Primary 58F10; Secondary 57E99
MathSciNet review: 0438397
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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.

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Article copyright: © Copyright 1977 American Mathematical Society