Solving nonlinear recursions

A general method to map a polynomial recursion on a matrix linear one is suggested. The solution of the recursion is represented as a product of a matrix multiplied by the vector of initial values. This matrix is product of transfer matrices whose elements depend only on the polynomial and not on the initial conditions. The method is valid for systems of polynomial recursions and for polynomial recursions of arbitrary order. The only restriction on these recurrent relations is that the highest-order term can be written in explicit form as a function of the lowerorder terms ~existence of a normal form!. A continuous analog of this method is described as well. © 1996 American Institute of Physics. @S0022-2488~96!00111-9#