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A note on one-dimensional attracting sets in the three-sphere

Author: Joel C. Gibbons
Journal: Proc. Amer. Math. Soc. 31 (1972), 620-622
MSC: Primary 58F10
MathSciNet review: 0292109
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Abstract: This paper is an application of Williams' results for one-dimensional attracting sets to the three-sphere. Our objective is to classify up to $ \Omega $-conjugacy all diffeomorphisms of $ {S^3}$ satisfying Smale's axioms A and B and the condition that the nonwandering set consists of zero- and one-dimensional sinks and sources.

References [Enhancements On Off] (What's this?)

  • [1] R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473-487. MR 36 #897. MR 0217808 (36:897)
  • [2] -, Classification of one-dimensional attractors, Northwestern University, Evanston, Ill. (mimeographed notes).
  • [3] M. Hirsch et al., Neighborhoods of hyperbolic sets, Invent. Math. 9 (1969/70), 121-134. MR 41 #7232. MR 0262627 (41:7232)
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Keywords: Generalized solenoid, Alexander duality
Article copyright: © Copyright 1972 American Mathematical Society

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