Dynamics Seminar

Event Information Recurrence in Symbolic Dynamics
15:10 on Friday November 08, 2019
16:00 on Friday November 08, 2019
BA6183, Bahen Center, 40 St. George St.
Jonguk Yang

Stony Brook University

Consider the shift map acting on the space of one-sided sequences. Under this dynamics, a sequence exhibits one of three types of recurrence: non-recurrence, reluctant recurrence, or persistent recurrence. However, for a given arbitrary sequence, it can be difficult to determine which of these three possibilities will occur. To solve this problem, we introduce an algebraic structure on sequences called filtration that enables us to count recurrences efficiently. This then leads to the characterization of the strong recurrence property as a kind of infinite renormalizability of the shift map.