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A Class of Differentiable Toral Maps Which are Topologically Mixing
Proceedings of the American Mathematical Society
Vol. 127, No. 3 (Mar., 1999), pp. 915-924
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/119027
Page Count: 10
You can always find the topics here!Topics: Topological theorems, Differential topology, Mathematical manifolds, Homeomorphism, Topology, Eigenvalues, Dynamical systems, Absolute value, Mathematical theorems
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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).
Proceedings of the American Mathematical Society © 1999 American Mathematical Society