## A class of differentiable toral maps which are topologically mixing

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- by Naoya Sumi PDF
- Proc. Amer. Math. Soc.
**127**(1999), 915-924 Request permission

## Abstract:

We show that on the 2-torus $\mathbb {T}^{2}$ there exists a $C^{1}$ open set $\mathcal {U}$ of $C^{1}$ regular maps such that every map belonging to $\mathcal {U}$ is topologically mixing but is not Anosov. It was shown by Mañé that this property fails for the class of $C^{1}$ toral diffeomorphisms, but that the property does hold for the class of $C^{1}$ diffeomorphisms on the 3-torus $\mathbb {T}^{3}$. Recently Bonatti and Diaz proved that the second result of Mañé is also true for the class of $C^{1}$ diffeomorphisms on the $n$-torus $\mathbb {T}^{n}$ ($n\ge 4$).## References

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## Additional Information

**Naoya Sumi**- Affiliation: Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-03, Japan
- MR Author ID: 610209
- Email: sumi@math.metro-u.ac.jp
- Received by editor(s): November 26, 1996
- Received by editor(s) in revised form: June 26, 1997
- Communicated by: Mary Rees
- © Copyright 1999 American Mathematical Society
- 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