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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DOI:
https://doi.org/10.1090/S0002-9947-1976-0423420-9

Article copyright:
© Copyright 1976
American Mathematical Society