Symbolic dynamics in flows on three-manifolds

Franks, John

doi:10.1090/S0002-9947-1983-0704612-1

Symbolic dynamics in flows on three-manifolds
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Trans. Amer. Math. Soc. 279 (1983), 231-236 Request permission

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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