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