On global periodicity of difference equations

In this research, we consider a difference equation of order k 2 of the following form: yn+1 = f (yn, . . . , yn−k+1), n = 0, 1, 2, . . . . We develop necessary and/or sufficient conditions on f so that every solution of the above mentioned difference equation is periodic of the same period p.  2003 Elsevier Inc. All rights reserved.