论文标题
可逆动力学系统中的对称同质缠结具有正拓扑熵
Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy
论文作者
论文摘要
我们考虑$ \ Mathbb {r}^{2n} $中的可逆矢量字段，以使尤其反向对称的固定点集为$ n $ dimessional。让这样的系统具有平滑的一参数对称周期轨道家族，该家族在正常方向上是鞍形类型的。我们确定，当这个周期性轨道家族的稳定且不稳定的流形具有强烈的交叉相交时，拓扑熵是积极的。
We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of saddle type in normal directions. We establish that topological entropy is positive when the stable and unstable manifolds of this family of periodic orbits have a strongly-transverse intersection.
