Generalization of the Mandelbrot set: quaternionic quadratic maps

DOI10.1016/0960-0779(94)00163-KzbMath0912.58034WikidataQ127371008 ScholiaQ127371008MaRDI QIDQ1129379

Jagannathan Gomatam, Isobel McFarlane, John Doyle, Bonnie A. Steves

Publication date: 25 May 1999

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

zbMATH Keywords

stability domainsgeneralisation of the Mandelbrot setmultiple cyclesquaternionic quadratic maps

Mathematics Subject Classification ID

Topological dynamics (37B99) Dynamical systems over complex numbers (37F99)

Related Items (25)

Generalized quaternion M sets and Julia sets perturbed by dynamical noises ⋮ Control of the spatial Mandelbrot set generated in coupled map lattice ⋮ The generalized M-J sets for bicomplex numbers ⋮ On the convergence of multicomplex M-J sets to the Steinmetz hypersolids ⋮ Groebner basis, resultants and the generalized Mandelbrot set ⋮ Generalization of 3D Mandelbrot and Julia sets ⋮ Basins of attraction for a quadratic coquaternionic map ⋮ Imaginary scators quadratic mapping in 1+2D dynamic space ⋮ Dynamics of the coquaternionic maps \(x^2 + \mathsf{b}x\) ⋮ Control and synchronization of Mandelbrot sets in coupled map lattice ⋮ A GENERALIZED MANDELBROT SET FOR BICOMPLEX NUMBERS ⋮ Julia sets and Mandelbrot sets in Noor orbit ⋮ Symbolic dynamics in investigation of quaternionic Julia sets ⋮ QUATERNION M SET WITH NONE ZERO CRITICAL POINTS ⋮ Unnamed Item ⋮ The inverse iteration method for Julia sets in the 3-dimensional space ⋮ Imaginary Scators Bound Set Under the Iterated Quadratic Mapping in 1 + 2 Dimensional Parameter Space ⋮ The general quaternionic M-J sets on the mapping \(z\leftarrow z^{\alpha}+c \, (\alpha \in \mathbf N)\) ⋮ DYNAMICS OF A FAMILY OF QUADRATIC MAPS IN THE QUATERNION SPACE ⋮ GENERATION OF 3D JULIA SETS FROM SWITCHING POLYNOMIAL MAPS ⋮ ON A GENERALIZED FATOU–JULIA THEOREM IN MULTICOMPLEX SPACES ⋮ GENERALIZED MANDELBROT SETS FOR MEROMORPHIC COMPLEX AND QUATERNIONIC MAPS ⋮ ITERATION OF QUADRATIC MAPS ON MATRIX ALGEBRAS ⋮ Noise-perturbed quaternionic Mandelbrot sets ⋮ Iteration of Quadratic Maps on Coquaternions

Cites Work

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• Octonionic Julia sets
• Transition points in octonionic Julia sets
• On the dynamics of polynomial-like mappings

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