Constructing a concrete example of deformations in real projective structures: Bulging deformation. An earthquake deformation does not change the domain but bulging deformation will change the domain Ω. This corresponds to changing the vertical twisting parameter in Goldman’s coordinates. We want to investigate the dynamical property of this deformation, namely we want to show that the topological entropy remains bounded below but the entropy with respect to Sinai-Ruelle-Bowen measure goes to zero along the bulging deformation.
We want to study SRB measure using classical constructions splitting by conditional measures.
We want to study the relation between SRB measure entropy and the Hilber area of the projective surfaces.