Entropy dimension of measure preserving systems

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This combinatorial approach provides us with a new insight to analyze the entropy zero systems. We also define the dimension set of a system to investigate the structure of the randomness of the factors of a system. The notion of a uniform dimension in the class of entropy zero systems is introduced as a generalization of a K-system in the case of positive entropy. We investigate the joinings among entropy zero systems and prove the disjointness property among entropy zero systems using the dimension sets. Given a topological system, we compare topological entropy dimension with metric entropy dimension

A note on dimensional entropy for amenable group actions

In this short note, for countably infinite amenable group actions, we provide topological proofs for the following results: Bowen topological entropy (dimensional entropy) of the whole space equals the usual topological entropy along tempered F{\o}lner sequences; the Hausdorff dimension of an amenable subshift (for certain metric associated to some F{\o}lner sequence) equals its topological entropy. This answers questions by Zheng and Chen (Israel Journal of Mathematics 212 (2016), 895-911) and Simpson (Theory Comput. Syst. 56 (2015), 527-543)

Change and continuity: a morphological investigation of the creation of gated communities in post-reform Beijing

Alongside the socio-economic restructuring from a central planning system to a free market system, Beijing is being transformed into a “gated city of tomorrow” by building massive gated communities as a new form of private neighborhood planning and design. Although certain scholarly attentions have been received through the international debate over gated communities, there is a lack of systematic research on how these private urban landscapes are actually created at the micro-level and how their creation is related with historical development and social process. Therefore, this paper aims to contribute to an understanding of the origin and nature of the creation of gated communities in the setting of Beijing through a careful morphological investigation. More exactly, a set of private gated community schemes and a set of public produced neighborhood schemes of the early socialist period will be cross compared according to the major neighborhood morphological components in order to reveal the differences and similarities in their morphology, or in another sense the change and continuity in their planning and design. Meanwhile, the ideas and logics underpinning the changes will be accounted. Finally, design origins and the links between the morphological changes and the broad social process will be discussed in light of the research findings