Special alpha-limit sets on the interval

Abstract: For a noninvertible dynamical system (X,f) a point x can have many possible “pasts.” Special alpha limit sets were defined to contain all the limit points of all those backward orbits, and it turns out that for interval maps they have many good properties. For example, a point belongs to its own special alpha limit set (this is like “backward recurrence”) if and only if it is in the attracting center of the interval map [Hero, 1992].

One of the last papers by Sergei Kolyada proposes several conjectures and open problems about topological properties of special-alpha limit sets. This talk will address those problems. The project is joint work with Jana Hantáková.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University