| 一类Smale空间上的C~*-代数自同构的熵 |
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| 引用本文： | 侯成军. 一类Smale空间上的C~*-代数自同构的熵[J]. 数学学报, 2017, 60(1): 149-158 |
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| 作者姓名： | 侯成军 |
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| 作者单位： | 扬州大学数学科学学院 扬州 225002 |
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| 基金项目： | 国家自然科学基金资助项目（11271224,11371290,11371222） |
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| 摘 要： | Ian Putnam利用Smale空间上的渐近等价关系定义了广群C~*-代数及其典则自同构.本文在零维Smale空间的情形下,计算此类C~*-自同构的逼近熵,证明了相应C~*-动力系统关于CNT熵和逼近熵的"变分原理"成立.由此推演出此类Smale空间上的Bowen测度诱导的C~*-代数上的态是此典则自同构的唯一平衡态.
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| 关 键 词： | 拓扑熵 广群C~*-代数 有限类子平移 变分原理 |
The Entropies of the Canonical Automorphisms of C*-algebras from Some Smale Spaces |
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| Cheng Jun HOU. The Entropies of the Canonical Automorphisms of C*-algebras from Some Smale Spaces[J]. Acta Mathematica Sinica, 2017, 60(1): 149-158 |
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| Authors: | Cheng Jun HOU |
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| Affiliation: | School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, P. R. China |
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| Abstract: | We show that Voiculescu's topological entropy of the canonical automorphism of the C*-algebra arising from the asymptotic equivalence on every irreducible zero-dimensional Smale space is equal to the topological entropy of the original topological dynamics.For the related C*-dynamical system, we have the "variational principle" with respect to the CNT-entropy and the topological entropy, and also show that the state defined by the Bowen measure of the Smale space is the unique equilibrium state of the canonical automorphism. |
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| Keywords: | topological entropy groupoid C*-algebra subshift of finite type variational principle |
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