Multicomplex algebras on polynomials and generalized Hamilton dynamics

Generator of the complex algebra within the framework of general formulation obeys the quadratic equation. In this paper we explore multicomplex algebra with the generator obeying n-order polynomial equation with real coefficients. This algebra induces generalized trigonometry ((n+1)-gonometry), underlies of the nth order oscillator model and nth order Hamilton equations. The solution of an evolution equation generated by (n × n) matrix is represented via the set of (n + 1)-gonometric functions. The general form of the first constant of motion of the evolution equation is established. © 2005 Elsevier Inc. All rights reserved