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Topological conjugacy of Morse flows over finite Abelian groups. (English) Zbl 0677.54031
The problem of topological conjugacy of substitution flows has been solved by E. M. Coven and M. S. Keane [Trans. Am. Math. Soc. 162, 89-102 (1971; Zbl 0205.283)] and N. G. Markley [Isr. Math. 22, 332-353 (1975; Zbl 0317.54053)].
The author solves this problem for Morse flows over any finite Abelian group. Let G and $$G'$$ be such groups. It is shown that if $$(\Omega_ x,T)$$ and $$(\Omega_ y,T)$$ are Morse flows generated by Morse sequences x over G and y over $$G'$$, then they are topologically conjugate if, and only if, there exist blocks A, B with the same length, a generalized Morse sequence z over G and an isomorphism $$\phi$$ from G onto $$G'$$ such that $$x=A\times z$$ and $$y=B\times {\hat \phi}(z)$$ ($${\hat \phi}$$((g$${}_ i)^{\infty}_{i=0}))=(\phi (g_ i))^{\infty}_{i=0}$$.
Reviewer: W.R.Utz
##### MSC:
 54H20 Topological dynamics (MSC2010)
##### Keywords:
Morse flows over any finite Abelian group
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