BIFURCATION PHENOMENA OF THE NONASSOCIATIVE OCTONIONIC QUADRATIC

In this work we have performed an investigation into the limiting dyna mics and bifurcation phenomena of the non-associative octonionic quadr atic map. It displayed a wealth of nonlinear structure including fixed points, Hopf bifurcations, phase locking, periodic cycles, tori, nont rivial knots, loop doubling and tripling, infinite period doubling cas cades and hyperchaos. The evolution of the limiting structure was char acterized by the recursive interplay of these various bifurcation mech anisms, which led to the appearance of complex attracting structures. Connections from this behaviour to the theory of the Mandelbrot set we re established.