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Transactions of the American Mathematical Society

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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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  • [AS] D. Asimov, Round handles and non-singular Morse-Smale flows, Ann. of Math. (2) 102 (1975), 41-54. MR 0380883 (52:1780)
  • [B] R. Bowen, One-dimensional hyperbolic sets for flows, J. Differential Equations 12 (1972), 173-179. MR 0336762 (49:1535)
  • [B1-F2] P. Blanchard and J. Franks, An obstruction to the existence of certain dynamics in surface diffeomorphisms, Ergodic Theory Dynamical Systems 1 (1981), 255-260. MR 662468 (84b:58091)
  • [BF] R. Bowen and J. Franks, Homology for zero dimensional basic sets, Ann. of Math. (2) 106 (1977), 73-92. MR 0458492 (56:16692)
  • [C] Charles Conley, Isolated invariant sets and the Morse index, CBMS Regional Conf. Ser. in Math., no. 38, Amer. Math. Soc., Providence, R. I., 1978. MR 511133 (80c:58009)
  • [Fr] D. Fried, Subshifts on surfaces, Ergod. Th. Dynam. Sys. 2 (1982), 15-21. MR 684241 (84h:58122)
  • [PS] Charles Pugh and Michael Shub, Suspending subshifts, preprint. MR 648471 (83h:58078)
  • [R] D. Rolfsen, Knots and links, Publish or Perish, Berkeley, Calif., 1976. MR 0515288 (58:24236)
  • [S] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014 (37:3598)
  • [Wms] R. Williams, Classification of subshifts of finite type, Ann. of Math. (2) 98 (1973), 120-153; Errata, ibid. 99 (1974), 380-381. MR 0331436 (48:9769)

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Article copyright: © Copyright 1983 American Mathematical Society

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