A quasi-Anosov diffeomorphism that is not Anosov
Author:
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.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
http://www.ams.org/tran/1976-223-00/S0002-9947-1976-0423420-9/S0002-9947-1976-0423420-9.pdf
Reference10 articles.
1. Differentiably Ω-stable diffeomorphisms;Franks, John;Topology,1972
2. On invariant subsets of hyperbolic sets;Hirsch, Morris W.,1970
3. Stable manifolds and hyperbolic sets;Hirsch, Morris W.,1970
4. Expansive diffeomorphisms;Mañé, Ricardo,1975
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