关于标准族椭圆岛的圈性
On cyclicity one elliptic islands of the Standard family
摘要：
我们研究丰度的一类特殊的椭圆形岛屿（称为循环一椭圆形岛屿）的标准家庭的面积保持大参数值，即远离KAM政权的同胚。在一个有界的参数值集外，我们证明了无穷多个这样的岛共存的参数值集的勒贝格测度为零。另一方面，我们构造了一个任意大参数值的正豪斯多夫维数集，使得相关的标准映射允许无穷多个循环度为1的椭圆岛，其中心聚集在一个局部极大双曲集上.
英文摘要：
We study abundance of a special class of elliptic islands (called cyclicity one elliptic islands) for the Standard family of area preserving diffeomorphisms for large parameter values, i.e. far from the KAM regime. Outside a bounded set of parameter values, we prove that the Lebesgue measure of the set of parameter values for which an infinite number of such islands coexist is zero. On the other hand we construct a positive Hausdorff dimension set of arbitrarily large parameter values for which the associated standard map admits infinitely many elliptic islands of cyclicity one, whose centers accumulate on a locally maximal hyperbolic set.
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