旋转集与熵
Rotation set and Entropy
摘要：
1991年Llibre和MacKay证明了：如果$f$是2-torus同胚同胚，且$f$的旋转集有非空内部，则$f$有正的拓扑熵.在这里，我们给出了一个类逆定理。在$f$拓扑传递不可约的条件下，证明了2-环面$C^{1+ α}$与正拓扑熵单位元同构的旋转集的内部不为空.我们还给出了例子，表明这些假设是必要的。
英文摘要：
In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological entropy. Here, we give a converselike theorem. We show that the interior of the rotation set of a 2-torus $C^{1+ α}$ diffeomorphism isotopic to identity of positive topological entropy is not empty, under the additional hypotheses that $f$ is topologically transitive and irreducible. We also give examples that show that these hypotheses are necessary.
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