  We study the dynamics of a class of endomorphisms of A^N which restricts,
when N = 1, to the class of unicritical polynomials. Over the complex numbers,
we obtain lower bounds on the sum of Lyapunov exponents, and a statement which
generalizes the compactness of the Mandelbrot set. Over the algebraic numbers,
we obtain estimates on the critical height, and over general algebraically
closed fields we obtain some rigidity results for post-critically finite
morphisms of this form.
