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http://dx.doi.org/10.4134/BKMS.2002.39.2.333

TOPOLOGICAL CONJUGACY OF DISJOINT FLOWS ON THE CIRCLE  

Cieplinski, Krzysztof (Institute of Mathematics, Pedagogical University)
Publication Information
Bulletin of the Korean Mathematical Society / v.39, no.2, 2002 , pp. 333-346 More about this Journal
Abstract
Let $F={F^v:S^1->S^1,v\in\; V$ and $g={G^v:S^1->S^1,v\in\; V$ be disjoint flows defined on the unit circle $S^1$, 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 codition for topological conjugacy of disjoint flows i.e., the existence of a homeomorphism $\Gamma:S^1->S^1$ 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;
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