## “Notions of recurrence and transitivity for discrete dynamical systems”

Wednesday, October 9, 2019, h. 12:30 - Room 2AB45 - Jim Wiseman (Agnes Scott College, Decatur GA)

Abstract

By iterating a continuous function $f:X \to X$, we obtain a dynamical system on the space $X$. We are interested in the long-term behavior of points in this system. Of particular importance is recurrent and transitive behavior. We will consider some simple notions of recurrence and transitivity (points that are periodic, nonwandering, chain recurrent, strong chain recurrent, or generalized recurrent) and see how they are related to each other, and to the mixing structure of the dynamical system. Finally, we will look at explosions in the generalized recurrent set

(joint work with Anna Florio and Olga Bernardi).