Infinite Specification and Distributional Chaos in the Baire Space
Keywords:
Baire space, chaotic pair, distributional chaos, Schweizer-Smital chaos, specification propertyAbstract
Both distributional chaos and the specification property have been the subject of much inquiry in dynamical systems in the last 50 years. Several results link the two properties in compact dynamical systems. In this paper, we focus our study on the connection between the specification property and distributional chaos on a non-compact dynamical system. Specifically, we examine these properties on a shift space over a countable alphabet with the product topology and the usual shift map, which is known as the Baire space. We show that in this context a subshift with the infinite specification property must have distributional chaos.
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