Amalgamated free products of circle actions can be defined to produce minimal actions with at most 2n fixed points under orbit and index assumptions.
Tukia,Homeomorphic conjugates of Fuchsian groups, J
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Amalgamated Free Products of Circle Actions with a Bounded Number of Fixed Points
Amalgamated free products of circle actions can be defined to produce minimal actions with at most 2n fixed points under orbit and index assumptions.