Editing Dynamical system (section)

===Rectification===
A flow in most small patches of the phase space can be made very simple.  If ''y'' is a point where the vector field ''v''(''y'')&nbsp;≠&nbsp;0, then there is a change of coordinates for a region around ''y'' where the vector field becomes a series of parallel vectors of the same magnitude.  This is known as the rectification theorem.

The ''rectification theorem'' says that away from [[Mathematical singularity|singular points]] the dynamics of a point in a small patch is a straight line.  The patch can sometimes be enlarged by stitching several patches together, and when this works out in the whole phase space ''M'' the dynamical system is ''integrable''.  In most cases the patch cannot be extended to the entire phase space.  There may be singular points in the vector field (where ''v''(''x'')&nbsp;=&nbsp;0); or the patches may become smaller and smaller as some point is approached. The more subtle reason is a global constraint, where the trajectory starts out in a patch, and after visiting a series of other patches comes back to the original one. If the next time the orbit loops around phase space in a different way, then it is impossible to rectify the vector field in the whole series of patches.