Symbolic dynamics in flows on three-manifolds

John M Franks

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

Symbolic dynamics in flows on three-manifolds

John M Franks^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 53 of basic sets corresponding to some matrices.

Original language	English (US)
Pages (from-to)	231-236
Number of pages	6
Journal	Transactions of the American Mathematical Society
Volume	279
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1983-0704612-1
State	Published - Jan 1 1983

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1983-0704612-1

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AB - 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 53 of basic sets corresponding to some matrices.

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Symbolic dynamics in flows on three-manifolds

Abstract

ASJC Scopus subject areas

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