论文标题
部分可观测时空混沌系统的无模型预测
Unobstructed embeddings in Hirzebruch surfaces
论文作者
论文摘要
本文继续研究由$ b \ in（0,1）$参数（符号爆炸的大小）参数的象征性Hirzebruch表面的椭圆形嵌入功能。 Cristofaro-Gardiner等。 （Arxiv：2004.13062）发现，如果Hirzebruch表面的嵌入函数具有无限的楼梯，则该功能等于楼梯累积点处的体积曲线。在这里，我们使用几乎要复曲面的纤维来在累积点上为无限定义的非理性$ b $ b $价值构建全额，这意味着这些$ b $是潜在的楼梯值。 $ b $ - 价值是通过Magill-McDuff-Weiler（Arxiv：2203.06453）中定义的一组阻塞类别定义的。阻塞性类别的递归，交织的结构与几乎旋转纤维中可能突变的序列之间存在对应关系。该结果用于Magill-McDuff-Weiler（Arxiv：2203.06453），以表明这些类是非凡的，并且这些$ b $值确实具有无限的楼梯。
This paper continues the study of the ellipsoid embedding function of symplectic Hirzebruch surfaces parametrized by $b \in (0,1)$, the size of the symplectic blow-up. Cristofaro-Gardiner, et al. (arxiv: 2004.13062) found that if the embedding function for a Hirzebruch surface has an infinite staircase, then the function is equal to the volume curve at the accumulation point of the staircase. Here, we use almost toric fibrations to construct full-fillings at the accumulation points for an infinite family of recursively defined irrational $b$-values implying these $b$ are potential staircase values. The $b$-values are defined via a family of obstructive classes defined in Magill-McDuff-Weiler (arxiv:2203.06453). There is a correspondence between the recursive, interwoven structure of the obstructive classes and the sequence of possible mutations in the almost toric fibrations. This result is used in Magill-McDuff-Weiler (arxiv:2203.06453) to show that these classes are exceptional and that these $b$-values do have infinite staircases.
