A new family of integrable differential systems in arbitrary dimension

Abstract: We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that illustrates the applicability of our approach. For instance, in the plane this list includes some Li\'enard, Lotka--Volterra and quadratic systems; in the space, some Kolmogorov, Rikitake and R\"ossler systems. Examples of complete integrable systems in higher dimensions are also provided.