Homotopy perturbations method: Theoretical as­pects and applications

The application of the homotopy perturbation method (HPM) in two different research's area has been proposed in this paper. First, the HPM has been used for approximate solving of the well-known implicit equation for electrostatic surface potential of MOSFET transistor. The approximate analytical solution obtained in this case has relative simple mathematical form, and simultaneously high degree of accuracy. Next, HPM has been applied in determination of the invariant measures (IMs) of the non-linear dynamical systems with chaotic behavior. The convergence and efficiency of this method have been confirmed and illustrated in some characteristic examples of chaotic mappings.