Dynamics Seminar

Event Information Combinatorial Description of Polynomial Julia Sets at the Boundary of Hyperbolic Components
15:10 on Monday October 22, 2018
16:00 on Monday October 22, 2018
BA6183, Bahen Center, 40 St. George St.
Jonguk Yang

Stony Brook University

Consider a polynomial (of any degree) with an attracting periodic point. We give a combinatorial description of its Julia set near the boundary of its hyperbolic component. Moreover, assuming that there is a unique boundary critical point (of any order), we can prove local connectivity at the boundary if the critical combinatorics is not strongly recurrent. Lastly, we characterize the strong recurrence property in terms of a new kind of renormalization acting on the Bernoulli shift.