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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Symbolic dynamics in flows on three-manifolds

Author: John Franks
Journal: Trans. Amer. Math. Soc. 279 (1983), 231-236
MSC: Primary 58F15; Secondary 58F25
MathSciNet review: 704612
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Abstract: This article deals with the problem of what suspended subshifts of finite type can be realized as a basic set of a nonsingular Smale flow on three-dimensional manifolds. It is shown that any suspended subshift can be realized in such a flow on some three-manifold. Also if signs reflecting orientation are included in the matrix of the subshift of finite type then there is an obstruction to the realization on $ {S^3}$ of basic sets corresponding to some matrices.

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Article copyright: © Copyright 1983 American Mathematical Society

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