A GENERALIZED MANDELBROT SET OF POLYNOMIALS OF TYPE Ed FOR BICOMPLEX NUMBERS

Abstract. We use a commutative generalization of complex numbers called bicomplex numbers to introduce the bicomplex dynamics of polynomials of type Ed, fc(w) = w(w + c)d. Rochon [9] proved that the Mandelbrot set of quadratic polynomials in bicomplex numbers of the form w2+c is connected. We prove that our generalized Mandelbrot set of polynomials of type Ed, fc(w) = w(w + c)d, is connected