ON MULTICORNS AND UNICORNS I: ANTIHOLOMORPHIC DYNAMICS, HYPERBOLIC COMPONENTS AND REAL CUBIC POLYNOMIALS

DOI10.1142/S0218127403008259zbMath1057.37047OpenAlexW2138622485WikidataQ29032073 ScholiaQ29032073MaRDI QIDQ4655511

Shizuo Nakane, Dierk Schleicher

Publication date: 8 March 2005

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

Full work available at URL: https://doi.org/10.1142/s0218127403008259

zbMATH Keywords

hyperbolic componentMultibrot setantiholomorphic dynamicsmulticornreal cubic polynomial

Mathematics Subject Classification ID

Related Items (23)

Non-landing parameter rays of the multicorns ⋮ Application of Fixed Point Iterative Methods to Construct Fractals and Anti-fractals ⋮ Analytic classification of germs of parabolic antiholomorphic diffeomorphisms of codimension k ⋮ On a family of rational perturbations of the doubling map ⋮ Symmetries of fractals revisited ⋮ Antiholomorphic perturbations of Weierstrass Zeta functions and Green’s function on tori ⋮ Cross-sections of the multicorns ⋮ Generalized fuzzy Mandelbrot and Mandelbar sets ⋮ Unnamed Item ⋮ On multicorns and unicorns II: bifurcations in spaces of antiholomorphic polynomials ⋮ Real saddle-node bifurcation from a complex viewpoint ⋮ Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn ⋮ Parabolic arcs of the multicorns: real-analyticity of Hausdorff dimension, and singularities of \(\mathrm{Per}_n(1)\) curves ⋮ Hubbard forests ⋮ Invisible tricorns in real slices of rational maps ⋮ Tricorns and multicorns of \(S\)-iteration scheme ⋮ Schwarz reflections and anti-holomorphic correspondences ⋮ Green’s function and anti-holomorphic dynamics on a torus ⋮ A note on the critical points of the localization landscape ⋮ Self-Similarity for the Tricorn ⋮ Orbit portraits of unicritical antiholomorphic polynomials ⋮ Discontinuity of Straightening in Anti-holomorphic Dynamics: I ⋮ Tips of tongues in the double standard family*

Cites Work

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• The iteration of cubic polynomials. I: The global topology of parameter space
• The iteration of cubic polynomials. II: Patterns and parapatterns
• Symmetries of fractals revisited
• On the structure of the Mandelbar set

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