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A quasi-Anosov diffeomorphism that is not Anosov


Authors: John Franks and Clark Robinson
Journal: Trans. Amer. Math. Soc. 223 (1976), 267-278
MSC: Primary 58F15
DOI: https://doi.org/10.1090/S0002-9947-1976-0423420-9
MathSciNet review: 0423420
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Abstract: In this note, we give an example of a diffeomorphism f on a three dimensional manifold M such that f has a property called quasi- Anosov but such that f does not have a hyperbolic structure (is not Anosov). Mañé has given a method of extending f to a diffeomorphism g on a larger dimensional manifold V such that g has a hyperbolic structure on M as a subset of V. This gives a counterexample to a question of M. Hirsch.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0423420-9
Article copyright: © Copyright 1976 American Mathematical Society

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