Topological entropy and bulging deformation of real projective structures on surface

In this paper, we study the deformation of strictly convex real projective structures on a closed surface. Especially, we study the deformation in terms of the entropy on bulging deformations and show that the topological entropy converges to some positive number as the parameter goes to infinity. As a byproduct we construct a sequence of divergent structures whose topological entropy converges to a designated number between 0 and 1. This result is complementary to the ones in [T. Zhang, Degeneration of Hitchin representations along internal sequences, Geom. Funct. Anal. 25 (2015) 1588–1645; X. Nie, Entropy degeneration of convex projective surfaces, Conform. Geom. Dyn. 19 (2015) 318–322] where they used internal parameter and cubic holomorphic differentials as parameters.