Anosov Actions of Isometry Groups on Lorentzian 2-Orbifolds

We prove a criterion of an Anosov action of the isometry group for compact Lorentzian -orbifolds. It is proved also that a non-compact complete flat Lorentzian -orbifold has an Anosov isometry if and only if its isometry group Lie acts improperly. The existence of chaotic behavior of such Anosov actions is investigated. It is shown that among smooth -orbifolds other than manifolds, only the ‘‘pillow’’ and the -cone admit the specified Lorentz metric with an Anosov action of the isometry group. The corresponding Lorentzian metrics and groups of isometries are indicated.