Research for Hilbert C*-bimodules and their application to complex dynamical systems

利用有理函数和自相似映射对riemann球上由动力系统构造的C^*-代数上的KMS态进行了分类。特别是对有理函数用例进行了完整的分类。利用希尔伯特C^*-双模构造了C^*-代数对应，它是有理函数的推广，并得到了C^*-代数的简单性和纯无穷性的充分条件。对于具有分支点的动力系统，如有理函数和自相似映射，构造了Hilbert C^*模的可数无限基的具体例子。

We classified KMS states on C^*-algebras constructed from the dynamical system on Riemannian sphere by rational functions and self-similar maps. Especially, we have made a complete classification for rational function cases. We constructed C^*-algebras using Hilbert C^*-bimodules for algebraic correspondences, which are generalization of rational functions, and have got sufficient conditions for simplicity and pure infiniteness of such C^*-algebras. We constructed concrete examples of countable infinite basis for Hilbert C^*-modules constructed from dynamical systems which have branch points, for example, rational functions and self-similar maps.