Bulletin of the
Korean Mathematical Society BKMS

Let ${\mathcal F}=\{F^{v}:\s \longrightarrow \s ,\:\: v\in V\}$ and ${\mathcal G}=\{G^{v}:\s \longrightarrow \s ,\:\: v\in V\}$ be disjoint flows defined on the unit circle $\s$, that is such flows that each their element either is the identity mapping or has no fixed point ($(V,\; +)$ is a $2$-divisible nontrivial abelian group). The aim of this paper is to give a necessary and sufficient condition for topological conjugacy of disjoint flows i.e., the existence of a homeomorphism $\Gamma :\s \longrightarrow \s$ satisfying \[ \Gamma \circ F^{v}=G^{v}\circ \Gamma ,\;\;\;\;\; v\in V. \] Moreover, under some further restrictions, we determine all such homeomorphisms.

Keywords: (disjoint, non-singular, singular, non-dense, dense, discrete) flow, degree, topological conjugacy, rotation number

MSC numbers: 20F38, 30D05, 37C15, 37E10, 39B12, 39B32, 39B72