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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1972-0292109-3
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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292109-3
Keywords: Generalized solenoid, Alexander duality
Article copyright: © Copyright 1972 American Mathematical Society