Poncelet's Closure Theorem and compositions of finite Blashke Products

We will briefly discuss the connection between generalized Poncelet's curves and Blashke Products (see "Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials", M. Hunziker, A. Martinez-Finkelshtein, T. Poe, and B. Simanek). Then I will introduce a result concerning the behaviour of Blashke products in the classic elliptical case and its applications.