论文标题
没有固定质量末端的椭圆点
No elliptic points from fixed prime ends
论文作者
论文摘要
我们考虑保留表面地图的区域，并扩展了马瑟的结果，即封闭了四个马鞍分支的平等。他认为椭圆固定点是Moser稳定的，而我们仅要求在此点的衍生物旋转与零不同的角度。文献中有许多结果需要以下假设：椭圆周期点是Moser稳定的，现在可以扩展到这些点的衍生物是不合理的旋转的情况。关键点是提供有关Cartwright和Littlewood的固定点定理的更多信息，以表明通过固定质量端获得的固定点不能是椭圆形的。然后，假设变得更容易验证：固定点的非变性和鞍座连接的不存在。作为一个应用程序，我们表明结果立即意味着对于标准地图家族，对于参数的所有值，除一个值外，主双曲线固定点具有同型点。我们还将结果扩展到具有边界的表面，以便适用于将地图返回到截面和损坏的图书分解的表面。
We consider area preserving maps of surfaces and extend Mather's result on the equality of the closure of the four branches of saddles. He assumed elliptic fixed points to be Moser stable, while we require only that the derivative at this points to be a rotation by an angle different from zero. There are many results in the literature which require the hypothesis that elliptic periodic points be Moser stable that now can be extended to the case that the derivative at these points be an irrational rotation. The key point is to give more information on Cartwright and Littlewood's fixed point theorem, to show that the fixed point obtained by a fixed prime end can not be elliptic. Hypotheses then became easier to verify: non degeneracy of fixed points and nonexistence of saddle connections. As an application we show that the result immediately implies that for the standard map family, for all values of the parameter, except one, the principal hyperbolic fixed point has homoclinic points. We also extend results to surfaces with boundary in order to be applicable to return maps to surfaces of section and broken book decompositions.
