A note on one-dimensional attracting sets in the three-sphere
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- by Joel C. Gibbons PDF
- Proc. Amer. Math. Soc. 31 (1972), 620-622 Request permission
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
- R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473–487. MR 217808, DOI 10.1016/0040-9383(67)90005-5 —, Classification of one-dimensional attractors, Northwestern University, Evanston, Ill. (mimeographed notes).
- M. Hirsch, J. Palis, C. Pugh, and M. Shub, Neighborhoods of hyperbolic sets, Invent. Math. 9 (1969/70), 121–134. MR 262627, DOI 10.1007/BF01404552
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 620-622
- MSC: Primary 58F10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292109-3
- MathSciNet review: 0292109