Diffeomorphisms approximated by Anosov on the 2-torus and their SBR measures
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- by Naoya Sumi PDF
- Trans. Amer. Math. Soc. 351 (1999), 3373-3385 Request permission
Abstract:
We consider the $C^{2}$ set of $C^{2}$ diffeomorphisms of the 2-torus $\mathbb {T}^{2}$, provided the conditions that the tangent bundle splits into the directed sum $T\mathbb {T}^{2}=E^{s}\oplus E^{u}$ of $Df$-invariant subbundles $E^{s}$, $E^{u}$ and there is $0<\lambda <1$ such that $\Vert Df|_{E^{s}}\Vert <\lambda$ and $\Vert Df|_{E^{u}}\Vert \ge 1$. 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 $C^{2}$ set has no SBR measures. This is related to a result of Hu-Young.References
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Additional Information
- Naoya Sumi
- Affiliation: Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-03, Japan
- MR Author ID: 610209
- Email: sumi@math.metro-u.ac.jp
- Received by editor(s): February 10, 1997
- Published electronically: April 8, 1999
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1637098