Diffeomorphisms approximated by Anosov on the 2torus and their SBR measures
Author:
Naoya Sumi
Journal:
Trans. Amer. Math. Soc. 351 (1999), 33733385
MSC (1991):
Primary 58F11, 58F12, 58F15
Published electronically:
April 8, 1999
MathSciNet review:
1637098
Fulltext PDF Free Access
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Abstract: We consider the set of diffeomorphisms of the 2torus , 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 HuYoung.
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Additional Information
Naoya Sumi
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, MinamiOhsawa 11, Hachioji, Tokyo 19203, Japan
Email:
sumi@math.metrou.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002994799024265
PII:
S 00029947(99)024265
Keywords:
Anosov diffeomorphism,
SBR measure
Received by editor(s):
February 10, 1997
Published electronically:
April 8, 1999
Article copyright:
© Copyright 1999
American Mathematical Society
