Identical particles and strong dynamical localization on the Möbius strip

The classical and quantum versions of the kicked rotator with two identical particles are considered. The particle interaction is only through identification and its configuration space is a Möbius strip. The classical dynamics presents no localization, except for particular initial conditions. There is a family of possible quantizations for this system and we pay special attention to the bosonic and fermionic cases. It is numerically found that the dynamical localization persists even though its classical counterpart is never localized.