We present a method to investigate the off momentum effects on the single particle transverse dynamics in a non linear lattice. We show that the one turn map approach is suitable to describe the coupling between the nonlinearity and the off momentum. We prove that for a linear lattice with a single sextupole in the thin lens approximation, the Hénon map description can be proposed. The computation of the tune shift and non linear dispersion is presented. It is shown that the off momentum dynamic aperture can be related to the dynamic aperture of the Hénon map with the shifted tune. Extensions to the four dimensional case are briefly outlined.