A quasi-Anosov diffeomorphism that is not Anosov

Franks, John; Robinson, Clark

doi:10.1090/S0002-9947-1976-0423420-9

A quasi-Anosov diffeomorphism that is not Anosov
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by John Franks and Clark Robinson

Trans. Amer. Math. Soc. 223 (1976), 267-278

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

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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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