Chaoticity and invariant measures for a cell population model

We present a structured model of a cell reproduction system given by a partial differential equations with a nonlocal division term. This equation generates semiflows acting on some subspaces of locally integrable functions. We show that these semiflows possess invariant mixing measures positive on open sets. From this it follows that the system is chaotic, i.e., it has dense trajectories and each trajectory is unstable. We also show the chaoticity of this system in the sense of Devaney.