Minimal non-invertible maps on the pseudo-circle

In this article, we show that R.H. Bings pseudo-circle admits a minimal non-invertible map. This resolves a problem raised by Bruin, Kolyada and Snoha in the negative. The main tool is the Denjoy-Rees technique, further developed by Beguin-Crovisier-Le Roux, combined with detailed study into the structure of the pseudo-circle.