Abstract:In this paper we present a generalization of Poincaré's Rotation Theory of homeomorphisms of the circle to the case of onedimensional compact abelian groups which are solenoidal groups, i.e., groups which fiber over the circle with fiber a Cantor abelian group. We define rotation elements,à la Poincaré and discuss the dynamical properties of translations on these solenoidal groups. We also study the semiconjugation problem when the rotation element generates a dense subgroup of the solenoidal group. Finally, w… Show more
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