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 omega. 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.
Furthermore we want to show that along such a smooth one-parameter deformation, the measure entropy varies continuously. We suspect that it may vary analytically.