GENERALIZED MANDELBROT SETS FOR MEROMORPHIC COMPLEX AND QUATERNIONIC MAPS

DOI10.1142/S0218127402005443zbMath1043.37038OpenAlexW2004495154MaRDI QIDQ4736262

Walter Buchanan, Bonnie A. Steves, Jagannathan Gomatam

Publication date: 9 August 2004

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127402005443

zbMATH Keywords

stability analysisquaternionsrational mapsmeromorphic mapscycle setsinverse maps

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (11)

LINEAR GENERALIZED SYNCHRONIZATION OF SPATIAL JULIA SETS ⋮ Basins of attraction for a quadratic coquaternionic map ⋮ Dynamics of the coquaternionic maps \(x^2 + \mathsf{b}x\) ⋮ Accurate computation of periodic regions' centers in the general \(M\)-set with integer index number ⋮ QUATERNION M SET WITH NONE ZERO CRITICAL POINTS ⋮ 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 ⋮ ITERATION OF QUADRATIC MAPS ON MATRIX ALGEBRAS ⋮ Noise-perturbed quaternionic Mandelbrot sets ⋮ Iteration of Quadratic Maps on Coquaternions

Cites Work

• The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift
• Generalization of the Mandelbrot set: quaternionic quadratic maps
• Transition points in octonionic Julia sets
• Die Funktionentheorie der Differentialgleichungen \(\Delta u=0\) und \(\Delta\Delta u=0\) mit vier reellen Variablen
• A note on the Julia set of a rational function

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