论文标题
2道龙在2托上的传递性和马蹄铁的存在
Transitivity and the existence of horseshoes on the 2-torus
论文作者
论文摘要
我们研究了两个圆环的同态同态的传递性与拓扑混乱之间的关系。我们表明，如果$ \ mathbb {t}^2 $的瞬时同构同态对身份是同型的，并且既有固定点，又有一个未固定的点，那么它具有拓扑马蹄。我们还表明，如果$ \ mathbb {t}^2 $的传递同源物与dehn Twist是同质的，那么它是Aperiodic的，或者具有拓扑组合。
We study the relationship between transitivity and topological chaos for homeomorphisms of the two torus. We show that if a transitive homeomorphism of $\mathbb{T}^2$ is homotopic to the identity and has both a fixed point and a periodic point which is not fixed, then it has a topological horseshoe. We also show that if a transitive homeomorphims of $\mathbb{T}^2$ is homotopic to a Dehn twist, then either it is aperiodic or it has a topological horseshoe.
