Homomorphisms of symbolic dynamical systems

Klein, Benjamin G.

doi:10.1007/bf01706082

Cited by 43 publications

(6 citation statements)

References 10 publications

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“…The minimality of (tf(to), a) was first observed by Gottschalk [4] and the unique ergodicity by Klein [5]. Others, including Dekking [1] and Michel [7], have extended these results to more general situations than those discussed here.…”

Section: Heresupporting

confidence: 59%

A covering cocycle which does not grow linearly

Madden¹

1995

Trans. Amer. Math. Soc.

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A cocycle h : X x Zm-► R" of a Zm action on a compact metric space, provides an R" suspension flow (analogous to a flow under a function) on a space Xh which may not be Hausdorff or even 7".. Linear growth of h guarantees that X¡, is a Hausdorff space; when m = n , linear growth is a consequence of Xn being Hausdorff and a covering condition. This paper contains the construction of a cocycle h : X x Z-» R2 which does not grow linearly yet produces a locally compact Hausdorff space with the covering condition. The Z action used in the construction is a substitution minimal set.

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Section: Heresupporting

confidence: 59%

A covering cocycle which does not grow linearly

Madden¹

1995

Trans. Amer. Math. Soc.

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“…License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use The minimality of (tf(to), a) was first observed by Gottschalk [4] and the unique ergodicity by Klein [5]. Others, including Dekking [1] and Michel [7], have extended these results to more general situations than those discussed here.…”

Section: Heresupporting

confidence: 52%

A Covering Cocycle which Does not Grow Linearly

Madden¹

1995

Transactions of the American Mathematical Society

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Abstract.A cocycle h : X x Zm -► R" of a Zm action on a compact metric space, provides an R" suspension flow (analogous to a flow under a function) on a space Xh which may not be Hausdorff or even 7". . Linear growth of h guarantees that X¡, is a Hausdorff space; when m = n , linear growth is a consequence of Xn being Hausdorff and a covering condition. This paper contains the construction of a cocycle h : X x Z -» R2 which does not grow linearly yet produces a locally compact Hausdorff space with the covering condition. The Z action used in the construction is a substitution minimal set.

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“…Michel [7] has shown that any substitution minimal set is strictly ergodic, and Klein [6] obtained this result earlier for substitutions of constant length. For substitution minimal sets which are generalized Morse minimal sets, this is also easily derivable from our Theorem 4.…”

Section: Jgmentioning

confidence: 99%

“…If we identify the sequence x with a sequence v on the four symbols 2, 4,6,8 by the rule 0 -» 2, 1 -> 4, 2 -> 8, 3 -» 6, then it can be shown that v is the sequence constructed by Kakutani [4, Example 2]. There it is constructed from the formula y(k) = the last nonzero digit in the decimal expansion of &!…”

Section: Jgmentioning

confidence: 99%

The structure of generalized Morse minimal sets on 𝑛 symbols

Martin¹

1977

Trans. Amer. Math. Soc.

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Abstract. A class of bisequences on n symbols is constructed which includes the generalized Morse sequences introduced by Keane. Those which give rise to strictly ergodic sets are characterized, and the spectrum of the shift operator on these systems is investigated. It is shown that in certain cases the shift operator has partly discrete and partly continuous spectrum. The theorems generalize results of Keane on generalized Morse sequences and a theorem of Kakutani regarding a particular strictly transitive sequence on four symbols. Another special case yields information on the spectrum of certain substitution minimal sets.

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Homomorphisms of symbolic dynamical systems

Cited by 43 publications

References 10 publications

A covering cocycle which does not grow linearly

A covering cocycle which does not grow linearly

A Covering Cocycle which Does not Grow Linearly

The structure of generalized Morse minimal sets on 𝑛 symbols

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