A class of differentiable toral maps

which are topologically mixing

Author:
Naoya Sumi

Journal:
Proc. Amer. Math. Soc. **127** (1999), 915-924

MSC (1991):
Primary 58F12

MathSciNet review:
1469436

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that on the 2-torus there exists a open set of regular maps such that every map belonging to is topologically mixing but is not Anosov. It was shown by Mañé that this property fails for the class of toral diffeomorphisms, but that the property does hold for the class of diffeomorphisms on the 3-torus . Recently Bonatti and Diaz proved that the second result of Mañé is also true for the class of diffeomorphisms on the -torus ().

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Additional Information

**Naoya Sumi**

Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-03, Japan

Email:
sumi@math.metro-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-99-04608-0

Keywords:
Anosov differentiable map,
DA-map,
sensitive dependence on initial conditions,
topological mixing,
transversal homoclinic point

Received by editor(s):
November 26, 1996

Received by editor(s) in revised form:
June 26, 1997

Communicated by:
Mary Rees

Article copyright:
© Copyright 1999
American Mathematical Society