In this paper, we consider the orbital-reversibility problem for an n-dimensional vector field, which consists in determining if there exists a time-reparametrization that transforms the vector field into a reversible one. We obtain an orbital normal form that brings out the invariants that prevent the orbital-reversibility. Hence, we obtain a necessary condition for a vector field to be orbital-reversible. Namely, the existence of an orbital normal form which is reversible to the change of sign in some of the state variables. The necessary condition provides an algorithm, based on the vanishing of the orbital normal form terms that avoid the orbital-reversibility, that is applied to some families of planar and three-dimensional systems.

在本文中，我们考虑n维矢量场的轨道可逆性问题，该问题在于确定是否存在将矢量场转换为可逆场的时间重新参数化。我们获得了一个轨道范式，该范式带出了防止轨道可逆性的不变性。因此，我们获得了矢量场是轨道可逆的必要条件。即，存在一些状态变量中可逆于符号变化的轨道正态形式的存在。必要条件提供了一种算法，该算法基于避免绕轨道可逆性的轨道法线形式项的消失，将其应用于平面和三维系统的某些族。