We define invariants of two dimensional projectively Anosov diffeomorphisms. The invariants are defined by the topology of the space of circles tangent to an invariant subbundle and are preserved under homotopy of projectively Anosov diffeomorphisms. As an application, we show that the invariant subbundle is not uniquely integrable and two distinct periodic orbits exist if certain invariants do not vanish.
Masayuki ASAOKA. "Invariants of two-dimensional projectively Anosov diffeomorphisms and their applications." J. Math. Soc. Japan 59 (3) 603 - 648, July, 2007. https://doi.org/10.2969/jmsj/05930603