Subevent of CT Session #1
‟Interruptions and Chaos on Non-smooth fans” by Jimmy Zakeršnik <jimmy.zakersnik1@um.si>, University of Maribor, Slovenia
Abstract:
In this talk, we present the construction and dynamical properties of a family of arcwise connected continua known as fans. Firstly, we present a construction that, for any smooth fan $X$ containing a top and at least one accumulating leg, produces an uncountable family of pairwise non-homeomorphic non-smooth fans, such that the set of endpoints of each of them is homeomorphic to the set of endpoints of $X$. Secondly, we show that this construction preserves certain dynamical properties such as topological mixing, and some types of chaos. Finally, we apply the results of the paper on a few well-known examples.