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A Class of Differentiable Toral Maps Which are Topologically Mixing

Naoya Sumi
Proceedings of the American Mathematical Society
Vol. 127, No. 3 (Mar., 1999), pp. 915-924
Stable URL: http://www.jstor.org/stable/119027
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Class of Differentiable Toral Maps Which are Topologically Mixing
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Abstract

We show that on the 2-torus T2 there exists a C1 open set U of C1 regular maps such that every map belonging to U is topologically mixing but is not Anosov. It was shown by Mañé that this property fails for the class of C1 toral diffeomorphisms, but that the property does hold for the class of C1 diffeomorphisms on the 3-torus T3. Recently Bonatti and Diaz proved that the second result of Mañé is also true for the class of C1 diffeomorphisms on the n-torus T4 (n ≥ 4).

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