Connectedness of the tricorn

DOI10.1017/S0143385700007409zbMath0781.58026MaRDI QIDQ3140466

Shizuo Nakane

Publication date: 13 February 1994

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

connectednessdynamicsquasiconformal mapsMandelbar settricornfamily of antiquadratic maps

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Quasiconformal mappings in the complex plane (30C62) Proper holomorphic mappings, finiteness theorems (32H35)

Related Items (13)

Non-landing parameter rays of the multicorns ⋮ Symmetries of fractals revisited ⋮ Antiholomorphic perturbations of Weierstrass Zeta functions and Green’s function on tori ⋮ Cross-sections of the multicorns ⋮ Dynamics of Schwarz Reflections: The Mating Phenomena ⋮ Distribution of postcritically finite polynomials III: Combinatorial continuity ⋮ On multicorns and unicorns II: bifurcations in spaces of antiholomorphic polynomials ⋮ Hausdorff Convergence and the Limit Shape of the Unicorns ⋮ 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 ⋮ Self-Similarity for the Tricorn ⋮ Orbit portraits of unicritical antiholomorphic polynomials ⋮ Discontinuity of Straightening in Anti-holomorphic Dynamics: I

Cites Work

• On the structure of the Mandelbar set

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