Reeb components with complex leaves and their symmetries I : The automorphism groups and Schr\"oder's equation on the half line
Geometric Topology
2016-05-31 v1 Complex Variables
Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1605.08977,
title = {Reeb components with complex leaves and their symmetries I : The automorphism groups and Schr\"oder's equation on the half line},
author = {Tomohiro Horiuchi and Yoshihiko Mitsumatsu},
journal= {arXiv preprint arXiv:1605.08977},
year = {2016}
}
Comments
34 pages, 2 figures, updated version from arXiv:1508.07162 and arXiv:1511.08985