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On conjugacy of disjoint iteration groups on the unit circle. (English) Zbl 0945.39006
The iteration groups $$\{F^t\}$$ and $$\{G^t\}$$ are conjugate if there exists a homeomorphism $$h$$ such that $$h \circ F^t = G^t \circ h$$ for all $$t\in \mathbb R.$$ The author offers necessary and sufficient conditions for conjugacy of iteration groups on the unit circle.

MSC:
 37E10 Dynamical systems involving maps of the circle 39B12 Iteration theory, iterative and composite equations 26A18 Iteration of real functions in one variable 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems