Associators in generalized octonionic maps. (English) Zbl 0772.58034
Summary: Generalizing previous work, we show that structural transitions are a general property of a large class of octonionic maps. They can thus be used as an indicator of non-associativity in an octonionic map.
MSC:
37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
37B99 | Topological dynamics |
30D05 | Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable |
References:
[1] | Griffin, C. J.; Joshi, G. C., Octonionic Julia sets, Chaos, Solitons & Fractals, 2, 11-24 (1992) · Zbl 0788.30038 |
[2] | Griffin, C. J.; Joshi, G. C., Transition points in octonionic Julia sets, Chaos, Solitons & Fractals, 3, 1, 67-88 (1993) · Zbl 0772.58035 |
[3] | Blanchard, P., Complex analytic synamics on the Riemann sphere, Bull. Am. Math. Soc., 11, 85-141 (1984) · Zbl 0558.58017 |
[4] | Sullivan, D., Quasiconformal homeomorphisms and dynamics I, II, III IHES (1983), preprints |
[5] | Mandelbrot, B., The Fractal Geometry of Nature (1982), Freeman: Freeman San Francisco · Zbl 0504.28001 |
[6] | Devaney, R. L.; Krych, M., Dynamics of exp \((z)\), Ergodic Theory Dynamic Sys., 4, 35-42 (1984) · Zbl 0567.58025 |
[7] | Devaney, R. L., Julia sets and bifurcation diagrams for exponential maps, Bull. Am. Math. Soc., 11, 167-171 (1984) · Zbl 0542.58021 |
[8] | Anderson, R.; Joshi, G. C., Quaternions and the heuristic role of mathematical structures in physics, (Essays in Physics (June 1993), University of Melbourne), preprint UM-P-92/61, to appear |
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