Matter Confinement Mechanism in de Sitter Brane

The geodesic equation in induced matter theory with de Sitter brane is described. It is shown that the extra forces do not change the four-impulse of massive particles. We also show that the variation of length of the 4-velocity of a test particle in de Sitter brane along the extra dimensions could remain finite resulting in a fluctuating component and hence keeping the particle inside the 4D spacetime and within the observable physics. In fact, the extra components trace closed orbits keep them finite in length. All of these are formulated in the framework of a dynamical system and we characterize the behaviour of the integral curves of this system.