论文标题
圆环上的Anosov地图的拓扑和平滑分类
Topological and smooth classification of Anosov maps on torus
论文作者
论文摘要
在本文中，我们对圆环上的不可变形Anosov地图进行了完整的拓扑和平滑分类。我们表明，当且仅当它们相应的周期点在稳定捆绑包上具有相同的lyapunov指数时，在拓扑上，圆环上的两个不可变形的Anosov地图是拓扑结合的。作为推论，如果两个$ c^r $不可固化的曲线地图是拓扑结合的，则与稳定的叶面沿$ c^r $ -smooth。此外，我们表明，圆环上不可变的Anosov地图的平滑共轭类完全由周期性的回报式地图的雅各布人确定。
In this paper, we give a complete topological and smooth classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topologically conjugate if and only if their corresponding periodic points have the same Lyapunov exponents on the stable bundles. As a corollary, if two $C^r$ non-invertible Anosov maps on torus are topologically conjugate, then the conjugacy is $C^r$-smooth along the stable foliation. Moreover, we show that the smooth conjugacy class of a non-invertible Anosov map on torus is completely determined by the Jacobians of return maps at periodic points.
