Entropy structure
Entropy structure
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DOI：
10.1007/bf02787825
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发表时间：
2005-01-01
影响因子：
1
通讯作者：
Downarowicz, T
中科院分区：
文献类型：
--
作者：
Downarowicz, T
通过研究不同尺度上熵的出现，我们提出了“熵结构”作为拓扑动力系统熵理论的一种主不变量。熵结构是不变测度单形上的函数序列h（k），其收敛于熵函数h并且福尔斯落入由捕获“收敛中的非均匀性类型”的自然等价关系定义的显著等价类。熵结构恢复了几个现有的不变量，包括符号扩展熵h（性别）和Misiurewicz参数h*。Misiurewicz、Katok、Brin-Katok、纽豪斯、Romagnoli、Omstein-Weiss和其他人的熵理论都产生候选序列（h（k））;我们确定这些序列中哪些表现出正确的收敛类型，从而成为熵结构。令人满意的序列之一产生于熵理论的一个新的治疗严格的连续函数（在分区或覆盖的地方）。结果允许计算符号扩展熵，而无需参考零维扩展。对渐近h-扩张性的性质给出了新的解释。
Investigating the emergence of entropy on different scales, we propose an "entropy structure" as a kind of master invariant for the entropy theory of topological dynamical systems. An entropy structure is a sequence of functions h(k) on the simplex of invariant measures which converges to the entropy function h and which falls into a distinguished equivalence class defined by a natural equivalence relation capturing the "type of nonuniformity in convergence". An entropy structure recovers several existing invariants, including the symbolic extension entropy h(sex) and the Misiurewicz parameter h*. Entropy theories of Misiurewicz, Katok, Brin-Katok, Newhouse, Romagnoli, Omstein-Weiss and others all yield candidate sequences (h(k)); we determine which of these exhibit the correct type of convergence and hence become entropy structures. One of the satisfactory sequences arises from a new treatment of entropy theory strictly in terms of continuous functions (in place of partitions or covers). The results allow the computation of symbolic extension entropy without reference to zero dimensional extensions. New light is shed on the property of asymptotic h-expansiveness.