一类Smale空间上的C~*-代数自同构的熵

The Entropies of the Canonical Automorphisms of C~*-algebras from Some Smale Spaces

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.

We show that Voiculescu＇s topological entropy of the canonical automor- phism 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 topologi- cal 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.