An effective construction of positive-entropy almost one-to-one topological extensions of the Chacón flow is given. These extensions have the property of almost minimal power joinings. For each possible value of entropy there are uncountably many pairwise non-conjugate such extensions.
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A combinatorial description of spectral isomorphisms between Morse flows is provided. We introduce the notion of a regular spectral isomorphism and we study some invariants of such isomorphisms. In the case of Morse cocycles taking values in $G = ℤ_p$, where p is a prime, each spectral isomorphism is regular. The same holds true for arbitrary finite abelian groups under an additional combinatorial condition of asymmetry in the defining Morse sequence, and for Morse flows of rank one. Rank one is shown to be a spectral invariant in the class of Morse flows.
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