One-dimensional quaternion homogeneous polynomial differential equations

In this paper we study the dynamics of real four-dimensional polynomial differential equations of the forms q =a qk q- m or q = qk a qm, where q,a are quaternions, q- is the conjugate of q, and k and m are non-negative integers. In many parts of the work the quaternion structure is used along the proofs. © 2009 American Institute of Physics.