Invariant manifolds in the measure-preserving mappings with three-dimensions

In this paper, we study the following three-dimensional mappings $$T:left{ begin{gathered} x_{n + 1} = x_n + y_n + B sin z_n , hfill y_{n + 1} = y_n + A sin x_{n + 1} , hfill z_{n + 1} = z_n + C sin y_{n + 1} + D, hfill end{gathered} right.left( {bmod 2Pi } right)$$ where A, B, C, D are parameters. When D>BC and 2π/D is an irrational number, we find numerically-two-dimensional and one-dimensional invariant manifolds, but when DBC and 2π/D is a rational number we find numerically one-dimensional manifolds and the fixed points for some cycles.