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- W3037917757 abstract "Geometric models and Teichmuller structures have been introduced for the space of smooth expanding circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one under the Techmuller metric. Moreover, the spaces of geometric models as well as the Teichmuller spaces can be described as the space of Holder continuous scaling functions and the space of continuous scaling functions on the dual symbolic space. The characterizations of these scaling functions have been also investigated. The Gibbs measure theory and the dual Gibbs measure theory for smooth expanding circle dynamics have been viewed from the geometric point of view. However, for uniformly symmetric circle dynamics, an appropriate Gibbs measure theory is unavailable, but a dual Gibbs type measure theory has been developed for the uniformly symmetric case. This development extends the dual Gibbs measure theory for the smooth case from the geometric point of view. In this survey article, We give a review of these developments which combines ideas and techniques from dynamical systems, quasiconformal mapping theory, and Teichmuller theory. There is a measure-theoretical version which is called $g$-measure theory and which corresponds to the dual geometric Gibbs type measure theory. We briefly review it too." @default.
- W3037917757 created "2020-07-02" @default.
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- W3037917757 date "2020-06-23" @default.
- W3037917757 modified "2023-09-27" @default.
- W3037917757 title "Geometric Gibbs theory" @default.
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- W3037917757 doi "https://doi.org/10.1007/s11425-019-1638-6" @default.
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