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摘要翻译：
我们证明了S.Saito的不动点公式是计算一个允许周期曲线的保面积曲面图的孤立周期点个数的有力工具。他关于I型和II型周期曲线的概念在我们的讨论中起着核心作用。本文建立了局部指数在映射迭代下的稳定性、II型周期曲线数目的有限性和I型周期曲线的不存在性的Shub-Sullivan型结果。结合这些结果，Saito公式蕴涵了无穷多个孤立周期点的存在性，这些孤立周期点的基数随着周期趋于无穷大而呈指数增长。
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英文标题：
《Area-Preserving Surface Dynamics and S. Saito's Fixed Point Formula》
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作者：
Katsunori Iwasaki and Takato Uehara
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We show that S. Saito's fixed point formula serves as a powerful tool for counting the number of isolated periodic points of an area-preserving surface map admitting periodic curves. His notion of periodic curves of types I and II plays a central role in our discussion. We establish a Shub-Sullivan type result on the stability of local indices under iterations of the map, the finiteness of the number of periodic curves of type II, and the absence of periodic curves of type I. Combined with these results, Saito's formula implies the existence of infinitely many isolated periodic points whose cardinality grows exponentially as period tends to infinity.
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PDF链接：
https://arxiv.org/pdf/0710.0706
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