# Combinatorial dynamics of the minimum entropy degree one circle maps depending on the rotation interval and its use as examples factory for graph maps

- Date:
- 18.03.19
- Times:
- 15:30
- Place:
- UAB - Dept. Matemàtiques (C1/-128)
- Speaker:
- Lluís Alsedà
- University:
- UAB

**Abstract**

The minimum entropy degree one circle maps depending on the rotation interval are known since 1988 [ALMM]. In this very technical seminar I will obtain the intertwinning of the the two extremal twist orbits of these maps when the endpoints of the interval are rational and I will show that this information characterizes completely the dynamics of such maps. In a second part I will show how to extend these maps to an arbitrary graph with a single circuit by essentially keeping the dynamics. This is a factory of particular examples with (a limited) dynamics analogous to circle dynamics of the the minimum entropy degree one circle maps.

[ALMM] Lluı́s Alsedà, Jaume Llibre, Francesc Mañosas, and Michal Misiurewicz. Lower bounds of the topological entropy for continuous maps of the circle of degree one. Nonlinearity, 1(3):463–479, 1988.