Diffeomorphisms approximated by Anosov on the

2-torus and their SBR measures

Author:
Naoya Sumi

Journal:
Trans. Amer. Math. Soc. **351** (1999), 3373-3385

MSC (1991):
Primary 58F11, 58F12, 58F15

DOI:
https://doi.org/10.1090/S0002-9947-99-02426-5

Published electronically:
April 8, 1999

MathSciNet review:
1637098

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the set of diffeomorphisms of the 2-torus , provided the conditions that the tangent bundle splits into the directed sum of -invariant subbundles , and there is such that and . Then we prove that the set is the union of Anosov diffeomorphisms and diffeomorphisms approximated by Anosov, and moreover every diffeomorphism approximated by Anosov in the set has no SBR measures. This is related to a result of Hu-Young.

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Additional Information

**Naoya Sumi**

Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-03, Japan

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

DOI:
https://doi.org/10.1090/S0002-9947-99-02426-5

Keywords:
Anosov diffeomorphism,
SBR measure

Received by editor(s):
February 10, 1997

Published electronically:
April 8, 1999

Article copyright:
© Copyright 1999
American Mathematical Society