Recurrence and the shadowing property

AbstractIn this paper, we study the relationship between the recurrent set and the shadowing property. We give a necessary condition for a homeomorphism restricted to its nonwandering set to have the shadowing property. Also, we consider a condition for an arbitrary homeomorphism to be a nonwandering homeomorphism. Finally, we consider homeomorphisms which cannot have the shadowing property

Competition and Innovation in Markets with Technology Leaders

In this article, we consider technology leaders (which are innovators) and technology followers (which are non-innovators) to provide a new theoretical explanation for the well-cited empirical evidence of an inverted-U relationship between competition and aggregate innovation. We consider a two-stage game with a deterministic Research and Development (R&D) process, where the leaders first determine their R&D investments simultaneously and then all leaders and followers determine their outputs simultaneously. We show that the inverted-U relationship between competition and aggregate innovation occurs if competition is affected by the number of technology followers. However, the presence of more technology leaders decreases individual R&D investments while increasing aggregate R&D investments. If the total number of firms remains the same but the composition of technology leaders and followers changes in favor of leaders (followers), individual R&D investments decrease (increase) but aggregate R&D investments increase (decrease). The relationship between competition and R&D investments can be U-shaped if the intensity of competition is measured by product substitutability. Contrary to the standard expectation, the presence of more firms may reduce welfare

A Niche Analysis of Three Interpersonal Communication Technologies: Examining the Competition among Facebook, Line, and Email

Adopting Dimmick’s niche theory as its theoretical framework, this study examined the gratifications obtained and gratification opportunities from Facebook, Line, and email to understand the competitive relationships among the three interpersonal media in Taiwan. This study first conducted twenty intensive interviews to construct questionnaire items to measure users’ gratifications obtained and gratification opportunities from the three media. Then, a telephone survey was conducted to collect data and 1042 valid calls were obtained. The data analysis shows that (1) among the three interpersonal media, Line had the widest niche breadth and the highest scores of competitive superiority and competed strongly with Facebook; and (2) the competitive superiority scores of a medium were a powerful predictor of the use history of that medium