Reeb components with complex leaves and their symmetries I : The automorphism groups and Schr\"oder's equation on the half line
Reeb components with complex leaves and their symmetries I : The automorphism groups and Schr\"oder's equation on the half line
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复叶Reeb分量及其对称性一：半线上的自同构群和施罗德方程
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Y. Mitsumatsu
中科院分区：
文献类型：
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作者：
Tomohiro Horiuchi;Y. Mitsumatsu
我们回顾了具有叶向复数结构的 Reeb 分量的标准 Hopf 构造，并确定了复杂叶维一情况下驯服 Reeb 分量的叶向全纯光滑自同构群。为此，我们在半线上求解施罗德型函数方程，以扩展微分同胚。结果，我们看到边界上具有平凡线性完整的一的自同构群包含无限维向量空间，而在非平凡线性完整的情况下，该群是有限维的。
We review the standard Hopf construction of Reeb components with leafwise complex structure and determine the group of leafwise holomorphic smooth automorphisms for tame Reeb components in the case of complex leaf dimension one. For this, we solve the Schr\"oder type functional equation on the half line for expanding diffeomorphism. As a result, we see that the automorphism group of one with trivial linear holonomy on the boundary contains an infinite dimensional vector space, while in the case of non-trivial linear holonomy the group is of finite dimensional.